Library

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:heavy_check_mark: test/aoj/aoj_2450.test.cpp

Depends on

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/2450"

#include "../../data_structure/lazy_segtree.hpp"
#include "../../graph/base.hpp"
#include "../../template/template.hpp"
#include "../../tree/heavy_light_decomposition.hpp"

using ebi::i64;
using ebi::LNF;

struct S {
    i64 sum;
    i64 lhs;
    i64 rhs;
    i64 ans;
    i64 sz;
};

using F = i64;
const F ID = LNF;

S op(S a, S b) {
    if (a.sz == 0) return b;
    if (b.sz == 0) return a;
    return {a.sum + b.sum, std::max(a.lhs, a.sum + b.lhs),
            std::max(a.rhs + b.sum, b.rhs),
            std::max(std::max(a.ans, b.ans), a.rhs + b.lhs), a.sz + b.sz};
}

S op_rev(S a, S b) {
    return op(b, a);
}

S e() {
    return {0, -LNF, -LNF, -LNF, 0};
}

S mapping(F f, S x) {
    if (f != ID) {
        x.sum = f * x.sz;
        if (f < 0) {
            x.lhs = f;
            x.rhs = f;
            x.ans = f;
        } else {
            x.lhs = x.rhs = x.ans = x.sum;
        }
    }
    return x;
}

F composition(F f, F g) {
    return (f == ID) ? g : f;
}

F id() {
    return ID;
}

int main() {
    int n, q;
    std::cin >> n >> q;
    std::vector<i64> w(n);
    for (int i = 0; i < n; i++) std::cin >> w[i];
    ebi::Graph<int> g(n);
    g.read_tree();
    ebi::heavy_light_decomposition hld(g);
    std::vector<S> vec(n);
    for (int i = 0; i < n; i++) {
        vec[hld.idx(i)] = {w[i], w[i], w[i], w[i], 1};
    }
    ebi::lazy_segtree<S, op, e, F, mapping, composition, id> seg1(vec);
    ebi::lazy_segtree<S, op_rev, e, F, mapping, composition, id> seg2(vec);
    F c = id();
    S ans = e();
    auto apply = [&](int u, int v) -> void {
        if (u > v) std::swap(u, v);
        seg1.apply(u, v, c);
        seg2.apply(u, v, c);
    };
    auto prod = [&](int l, int r) -> void {
        if (l <= r)
            ans = op(ans, seg1.prod(l, r));
        else
            ans = op(ans, seg2.prod(r, l));
    };
    while (q--) {
        int t, a, b;
        std::cin >> t >> a >> b >> c;
        a--;
        b--;
        if (t == 1) {
            hld.path_noncommutative_query(a, b, true, apply);
        } else {
            ans = e();
            hld.path_noncommutative_query(a, b, true, prod);
            std::cout << ans.ans << '\n';
        }
    }
}
#line 1 "test/aoj/aoj_2450.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/problems/2450"

#line 2 "data_structure/lazy_segtree.hpp"

/*
    reference:
   https://atcoder.github.io/ac-library/master/document_ja/lazysegtree.html
*/

#include <bit>

#include <cassert>

#include <cstdint>

#include <ranges>

#include <vector>


namespace ebi {

template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S),
          F (*composition)(F, F), F (*id)()>
struct lazy_segtree {
  private:
    void update(int i) {
        data[i] = op(data[2 * i], data[2 * i + 1]);
    }

    void all_apply(int k, F f) {
        data[k] = mapping(f, data[k]);
        if (k < sz) lazy[k] = composition(f, lazy[k]);
    }

    void push(int i) {
        all_apply(2 * i, lazy[i]);
        all_apply(2 * i + 1, lazy[i]);
        lazy[i] = id();
    }

  public:
    lazy_segtree(int n_) : lazy_segtree(std::vector<S>(n_, e())) {}
    lazy_segtree(const std::vector<S> &a)
        : n(a.size()),
          sz(std::bit_ceil(a.size())),
          lg2(std::countr_zero(std::uint32_t(sz))) {
        data = std::vector<S>(2 * sz, e());
        lazy = std::vector<F>(sz, id());
        for (int i : std::views::iota(0, n)) {
            data[sz + i] = a[i];
        }
        for (int i : std::views::iota(1, sz) | std::views::reverse) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < n);
        p += sz;
        for (int i = lg2; i >= 1; i--) push(p >> i);
        data[p] = x;
        for (int i = 1; i <= lg2; i++) update(p >> i);
    }

    S get(int p) {
        assert(0 <= p && p < n);
        p += sz;
        for (int i = lg2; i >= 1; i--) push(p >> i);
        return data[p];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= n);
        if (l == r) return e();

        l += sz;
        r += sz;

        for (int i = lg2; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, data[l++]);
            if (r & 1) smr = op(data[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() const {
        return data[1];
    }

    void apply(int p, F f) {
        assert(0 <= p && p < n);
        p += sz;
        for (int i = lg2; i >= 1; i--) push(p >> i);
        data[p] = mapping(f, data[p]);
        for (int i = 1; i <= lg2; i++) update(p >> i);
    }

    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= n);
        l += sz;
        r += sz;
        for (int i = lg2; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int memo_l = l, memo_r = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = memo_l;
            r = memo_r;
        }

        for (int i = 1; i <= lg2; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    template <class G> int max_right(int l, G g) {
        assert(0 <= l && l <= n);
        assert(g(e()));
        if (l == n) return n;
        l += sz;
        for (int i = lg2; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, data[l]))) {
                while (l < sz) {
                    push(l);
                    l = l << 1;
                    if (g(op(sm, data[l]))) {
                        sm = op(sm, data[l]);
                        l++;
                    }
                }
                return l - sz;
            }
            sm = op(sm, data[l]);
            l++;
        } while ((l & -l) != l);
        return n;
    }

    template <class G> int min_left(int r, G g) {
        assert(0 <= r && r <= n);
        assert(g(e()));
        if (r == 0) return 0;
        r += sz;
        for (int i = lg2; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && r % 2) r >>= 1;
            if (!g(op(data[r], sm))) {
                while (r < sz) {
                    push(r);
                    r = (r << 1) + 1;
                    if (g(op(data[r], sm))) {
                        sm = op(data[r], sm);
                        r--;
                    }
                }
                return r + 1 - sz;
            }
            sm = op(data[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int n, sz, lg2;
    std::vector<S> data;
    std::vector<F> lazy;
};

}  // namespace ebi

#line 2 "graph/base.hpp"

#line 4 "graph/base.hpp"
#include <iostream>
#line 7 "graph/base.hpp"

#line 2 "data_structure/simple_csr.hpp"

#line 4 "data_structure/simple_csr.hpp"
#include <utility>
#line 6 "data_structure/simple_csr.hpp"

namespace ebi {

template <class E> struct simple_csr {
    simple_csr() = default;

    simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
        : start(n + 1, 0), elist(elements.size()) {
        for (auto e : elements) {
            start[e.first + 1]++;
        }
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] += start[i];
        }
        auto counter = start;
        for (auto [i, e] : elements) {
            elist[counter[i]++] = e;
        }
    }

    simple_csr(const std::vector<std::vector<E>>& es)
        : start(es.size() + 1, 0) {
        int n = es.size();
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] = (int)es[i].size() + start[i];
        }
        elist.resize(start.back());
        for (auto i : std::views::iota(0, n)) {
            std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
        }
    }

    int size() const {
        return (int)start.size() - 1;
    }

    const auto operator[](int i) const {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }
    auto operator[](int i) {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }

    const auto operator()(int i, int l, int r) const {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }
    auto operator()(int i, int l, int r) {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }

  private:
    std::vector<int> start;
    std::vector<E> elist;
};

}  // namespace ebi
#line 9 "graph/base.hpp"

namespace ebi {

template <class T> struct Edge {
    int from, to;
    T cost;
    int id;
};

template <class E> struct Graph {
    using cost_type = E;
    using edge_type = Edge<cost_type>;

    Graph(int n_) : n(n_) {}

    Graph() = default;

    void add_edge(int u, int v, cost_type c) {
        assert(!prepared && u < n && v < n);
        buff.emplace_back(u, edge_type{u, v, c, m});
        edges.emplace_back(edge_type{u, v, c, m++});
    }

    void add_undirected_edge(int u, int v, cost_type c) {
        assert(!prepared && u < n && v < n);
        buff.emplace_back(u, edge_type{u, v, c, m});
        buff.emplace_back(v, edge_type{v, u, c, m});
        edges.emplace_back(edge_type{u, v, c, m});
        m++;
    }

    void read_tree(int offset = 1, bool is_weighted = false) {
        read_graph(n - 1, offset, false, is_weighted);
    }

    void read_parents(int offset = 1) {
        for (auto i : std::views::iota(1, n)) {
            int p;
            std::cin >> p;
            p -= offset;
            add_undirected_edge(p, i, 1);
        }
        build();
    }

    void read_graph(int e, int offset = 1, bool is_directed = false,
                    bool is_weighted = false) {
        for (int i = 0; i < e; i++) {
            int u, v;
            std::cin >> u >> v;
            u -= offset;
            v -= offset;
            if (is_weighted) {
                cost_type c;
                std::cin >> c;
                if (is_directed) {
                    add_edge(u, v, c);
                } else {
                    add_undirected_edge(u, v, c);
                }
            } else {
                if (is_directed) {
                    add_edge(u, v, 1);
                } else {
                    add_undirected_edge(u, v, 1);
                }
            }
        }
        build();
    }

    void build() {
        assert(!prepared);
        csr = simple_csr<edge_type>(n, buff);
        buff.clear();
        prepared = true;
    }

    int size() const {
        return n;
    }

    int node_number() const {
        return n;
    }

    int edge_number() const {
        return m;
    }

    edge_type get_edge(int i) const {
        assert(prepared);
        return edges[i];
    }

    std::vector<edge_type> get_edges() const {
        assert(prepared);
        return edges;
    }

    const auto operator[](int i) const {
        assert(prepared);
        return csr[i];
    }
    auto operator[](int i) {
        assert(prepared);
        return csr[i];
    }

  private:
    int n, m = 0;

    std::vector<std::pair<int, edge_type>> buff;

    std::vector<edge_type> edges;
    simple_csr<edge_type> csr;
    bool prepared = false;
};

}  // namespace ebi
#line 1 "template/template.hpp"
#include <bits/stdc++.h>

#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()

#line 2 "template/int_alias.hpp"

#line 4 "template/int_alias.hpp"

namespace ebi {

using ld = long double;
using std::size_t;
using i8 = std::int8_t;
using u8 = std::uint8_t;
using i16 = std::int16_t;
using u16 = std::uint16_t;
using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;

}  // namespace ebi
#line 2 "template/io.hpp"

#line 5 "template/io.hpp"
#include <optional>
#line 7 "template/io.hpp"

#line 2 "modint/base.hpp"

#include <concepts>
#line 6 "modint/base.hpp"

namespace ebi {

template <class T>
concept Modint = requires(T a, T b) {
    a + b;
    a - b;
    a * b;
    a / b;
    a.inv();
    a.val();
    a.pow(std::declval<long long>());
    T::mod();
};

template <Modint mint> std::istream &operator>>(std::istream &os, mint &a) {
    long long x;
    os >> x;
    a = x;
    return os;
}

template <Modint mint>
std::ostream &operator<<(std::ostream &os, const mint &a) {
    return os << a.val();
}

}  // namespace ebi
#line 9 "template/io.hpp"

namespace ebi {

template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &pa) {
    return os << pa.first << " " << pa.second;
}

template <typename T1, typename T2>
std::istream &operator>>(std::istream &os, std::pair<T1, T2> &pa) {
    return os >> pa.first >> pa.second;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &vec) {
    for (std::size_t i = 0; i < vec.size(); i++)
        os << vec[i] << (i + 1 == vec.size() ? "" : " ");
    return os;
}

template <typename T>
std::istream &operator>>(std::istream &os, std::vector<T> &vec) {
    for (T &e : vec) std::cin >> e;
    return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::optional<T> &opt) {
    if (opt) {
        os << opt.value();
    } else {
        os << "invalid value";
    }
    return os;
}

void fast_io() {
    std::cout << std::fixed << std::setprecision(15);
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
}

}  // namespace ebi
#line 2 "template/utility.hpp"

#line 5 "template/utility.hpp"

#line 8 "template/utility.hpp"

namespace ebi {

template <class T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <class T> T safe_ceil(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return (a / b) + 1;
    else
        return -((-a) / b);
}

template <class T> T safe_floor(T a, T b) {
    if (a % b == 0)
        return a / b;
    else if (a >= 0)
        return a / b;
    else
        return -((-a) / b) - 1;
}

constexpr i64 LNF = std::numeric_limits<i64>::max() / 4;

constexpr int INF = std::numeric_limits<int>::max() / 2;

const std::vector<int> dy = {1, 0, -1, 0, 1, 1, -1, -1};
const std::vector<int> dx = {0, 1, 0, -1, 1, -1, 1, -1};

}  // namespace ebi
#line 2 "template/debug_template.hpp"

#line 4 "template/debug_template.hpp"

namespace ebi {

#ifdef LOCAL
#define debug(...)                                                      \
    std::cerr << "LINE: " << __LINE__ << "  [" << #__VA_ARGS__ << "]:", \
        debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif

void debug_out() {
    std::cerr << std::endl;
}

template <typename Head, typename... Tail> void debug_out(Head h, Tail... t) {
    std::cerr << " " << h;
    if (sizeof...(t) > 0) std::cerr << " :";
    debug_out(t...);
}

}  // namespace ebi
#line 2 "tree/heavy_light_decomposition.hpp"

#line 6 "tree/heavy_light_decomposition.hpp"

#line 8 "tree/heavy_light_decomposition.hpp"

namespace ebi {

template <class T> struct heavy_light_decomposition {
  private:
    void dfs_sz(int v) {
        for (auto &e : g[v]) {
            if (e.to == par[v]) continue;
            par[e.to] = v;
            depth_[e.to] = depth_[v] + 1;
            dist[e.to] = dist[v] + e.cost;
            dfs_sz(e.to);
            sz[v] += sz[e.to];
            if (sz[e.to] > sz[g[v][0].to] || g[v][0].to == par[v])
                std::swap(e, g[v][0]);
        }
    }

    void dfs_hld(int v) {
        in[v] = num++;
        rev[in[v]] = v;
        for (auto e : g[v]) {
            if (e.to == par[v]) continue;
            nxt[e.to] = (e.to == g[v][0].to ? nxt[v] : e.to);
            dfs_hld(e.to);
        }
        out[v] = num;
    }

    // [u, v) パスの取得 (v は u の祖先)
    std::vector<std::pair<int, int>> ascend(int u, int v) const {
        std::vector<std::pair<int, int>> res;
        while (nxt[u] != nxt[v]) {
            res.emplace_back(in[u], in[nxt[u]]);
            u = par[nxt[u]];
        }
        if (u != v) res.emplace_back(in[u], in[v] + 1);
        return res;
    }

    // (u, v] パスの取得 (u は v の祖先)
    std::vector<std::pair<int, int>> descend(int u, int v) const {
        if (u == v) return {};
        if (nxt[u] == nxt[v]) return {{in[u] + 1, in[v]}};
        auto res = descend(u, par[nxt[v]]);
        res.emplace_back(in[nxt[v]], in[v]);
        return res;
    }

  public:
    heavy_light_decomposition(const Graph<T> &gh, int root_ = 0)
        : n(gh.size()),
          root(root_),
          g(gh),
          sz(n, 1),
          in(n),
          out(n),
          nxt(n),
          par(n, -1),
          depth_(n, 0),
          rev(n),
          dist(n, 0) {
        nxt[root] = root;
        dfs_sz(root);
        dfs_hld(root);
    }

    int idx(int u) const {
        return in[u];
    }

    int rev_idx(int i) const {
        return rev[i];
    }

    int la(int v, int k) const {
        while (1) {
            int u = nxt[v];
            if (in[u] <= in[v] - k) return rev[in[v] - k];
            k -= in[v] - in[u] + 1;
            v = par[u];
        }
    }

    int lca(int u, int v) const {
        while (nxt[u] != nxt[v]) {
            if (in[u] < in[v]) std::swap(u, v);
            u = par[nxt[u]];
        }
        return depth_[u] < depth_[v] ? u : v;
    }

    int jump(int s, int t, int i) const {
        if (i == 0) return s;
        int l = lca(s, t);
        int d = depth_[s] + depth_[t] - depth_[l] * 2;
        if (d < i) return -1;
        if (depth_[s] - depth_[l] >= i) return la(s, i);
        i = d - i;
        return la(t, i);
    }

    std::vector<int> path(int s, int t) const {
        int l = lca(s, t);
        std::vector<int> a, b;
        for (; s != l; s = par[s]) a.emplace_back(s);
        for (; t != l; t = par[t]) b.emplace_back(t);
        a.emplace_back(l);
        std::reverse(b.begin(), b.end());
        a.insert(a.end(), b.begin(), b.end());
        return a;
    }

    int root_of_heavy_path(int u) const {
        return nxt[u];
    }

    int parent(int u) const {
        return par[u];
    }

    T distance(int u, int v) const {
        return dist[u] + dist[v] - 2 * dist[lca(u, v)];
    }

    T distance_from_root(int v) const {
        return dist[v];
    }

    T depth(int v) const {
        return depth_[v];
    }

    bool at_path(int u, int v, int s) const {
        return distance(u, v) == distance(u, s) + distance(s, v);
    }

    std::pair<int, int> subtree_section(int v) const {
        return {in[v], out[v]};
    }

    bool is_subtree(int u, int v) const {
        return in[u] <= in[v] && in[v] < out[u];
    }

    template <class F>
    void path_noncommutative_query(int u, int v, bool vertex,
                                   const F &f) const {
        int l = lca(u, v);
        for (auto [a, b] : ascend(u, l)) f(a + 1, b);
        if (vertex) f(in[l], in[l] + 1);
        for (auto [a, b] : descend(l, v)) f(a, b + 1);
    }

    std::vector<std::pair<int, int>> path_sections(int u, int v,
                                                   bool vertex) const {
        int l = lca(u, v);
        std::vector<std::pair<int, int>> sections;
        for (auto [a, b] : ascend(u, l)) sections.emplace_back(a + 1, b);
        if (vertex) sections.emplace_back(in[l], in[l] + 1);
        for (auto [a, b] : descend(l, v)) sections.emplace_back(a, b + 1);
        return sections;
    }

    template <class F>
    int max_path(int u, int v, bool vertex, F binary_search) const {
        int prev = -1;
        int l = lca(u, v);
        for (auto [a, b] : ascend(u, l)) {
            a++;
            int m = binary_search(a, b);
            if (m == b) {
                prev = rev[b];
            } else {
                return (m == a ? prev : rev[m]);
            }
        }
        if (vertex) {
            int m = binary_search(in[l], in[l] + 1);
            if (m == in[l]) {
                return prev;
            } else {
                prev = l;
            }
        }
        for (auto [a, b] : descend(l, v)) {
            b++;
            int m = binary_search(a, b);
            if (m == b) {
                prev = rev[b - 1];
            } else {
                return m == a ? prev : rev[m - 1];
            }
        }
        return v;
    }

    template <class F> void subtree_query(int u, bool vertex, const F &f) {
        f(in[u] + int(!vertex), out[u]);
    }

    const std::vector<int> &dfs_order() const {
        return rev;
    }

    template <class ADD, class QUERY, class CLEAR, class RESET>
    void dsu_on_tree(const ADD &add, const QUERY &query, const CLEAR &clear,
                     const RESET &reset) const;

    std::vector<std::pair<int, int>> lca_based_auxiliary_tree_dfs_order(
        std::vector<int> vs) const;

    std::pair<std::vector<int>, Graph<T>> lca_based_auxiliary_tree(
        std::vector<int> vs) const;

  private:
    int n, root;
    Graph<T> g;
    std::vector<int> sz, in, out, nxt, par, depth_, rev;
    std::vector<T> dist;

    int num = 0;
};

}  // namespace ebi
#line 7 "test/aoj/aoj_2450.test.cpp"

using ebi::i64;
using ebi::LNF;

struct S {
    i64 sum;
    i64 lhs;
    i64 rhs;
    i64 ans;
    i64 sz;
};

using F = i64;
const F ID = LNF;

S op(S a, S b) {
    if (a.sz == 0) return b;
    if (b.sz == 0) return a;
    return {a.sum + b.sum, std::max(a.lhs, a.sum + b.lhs),
            std::max(a.rhs + b.sum, b.rhs),
            std::max(std::max(a.ans, b.ans), a.rhs + b.lhs), a.sz + b.sz};
}

S op_rev(S a, S b) {
    return op(b, a);
}

S e() {
    return {0, -LNF, -LNF, -LNF, 0};
}

S mapping(F f, S x) {
    if (f != ID) {
        x.sum = f * x.sz;
        if (f < 0) {
            x.lhs = f;
            x.rhs = f;
            x.ans = f;
        } else {
            x.lhs = x.rhs = x.ans = x.sum;
        }
    }
    return x;
}

F composition(F f, F g) {
    return (f == ID) ? g : f;
}

F id() {
    return ID;
}

int main() {
    int n, q;
    std::cin >> n >> q;
    std::vector<i64> w(n);
    for (int i = 0; i < n; i++) std::cin >> w[i];
    ebi::Graph<int> g(n);
    g.read_tree();
    ebi::heavy_light_decomposition hld(g);
    std::vector<S> vec(n);
    for (int i = 0; i < n; i++) {
        vec[hld.idx(i)] = {w[i], w[i], w[i], w[i], 1};
    }
    ebi::lazy_segtree<S, op, e, F, mapping, composition, id> seg1(vec);
    ebi::lazy_segtree<S, op_rev, e, F, mapping, composition, id> seg2(vec);
    F c = id();
    S ans = e();
    auto apply = [&](int u, int v) -> void {
        if (u > v) std::swap(u, v);
        seg1.apply(u, v, c);
        seg2.apply(u, v, c);
    };
    auto prod = [&](int l, int r) -> void {
        if (l <= r)
            ans = op(ans, seg1.prod(l, r));
        else
            ans = op(ans, seg2.prod(r, l));
    };
    while (q--) {
        int t, a, b;
        std::cin >> t >> a >> b >> c;
        a--;
        b--;
        if (t == 1) {
            hld.path_noncommutative_query(a, b, true, apply);
        } else {
            ans = e();
            hld.path_noncommutative_query(a, b, true, prod);
            std::cout << ans.ans << '\n';
        }
    }
}
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