icpc_library

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:heavy_check_mark: test/polynomial/Multipoint_Evaluation.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/multipoint_evaluation"

#include "../../fps/multipoint_evaluation.hpp"

#include "../../convolution/ntt.hpp"
#include "../../fps/fps.hpp"
#include "../../utility/modint.hpp"
#include "../../template/template.hpp"

namespace lib {

using mint = modint998244353;
using FPS = FormalPowerSeries<mint>;

void main_() {
    int n, m;
    std::cin >> n >> m;
    FPS f(n);
    rep(i,0,n) std::cin >> f[i].val();
    std::vector<mint> p(m);
    rep(i,0,m) std::cin >> p[i].val();
    auto fp = multipoint_evaluation<mint>(f, p);
    rep(i,0,m) {
        std::cout << fp[i].val() << " \n"[i == m-1];
    }
}

}  // namespace ebi

int main() {
    int t = 1;
    // std::cin >> t;
    while (t--) {
        lib::main_();
    }
    return 0;
}
#line 1 "test/polynomial/Multipoint_Evaluation.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/multipoint_evaluation"

#line 2 "fps/multipoint_evaluation.hpp"

#line 2 "fps/fps.hpp"

#line 2 "convolution/ntt4.hpp"

#line 2 "utility/modint.hpp"

#line 2 "template/template.hpp"

#include <bits/stdc++.h>

#define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++)
#define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--)
#define all(v) v.begin(), v.end()

using ll = long long;
using ld = long double;
using ull = unsigned long long;

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

namespace lib {

using namespace std;

}  // namespace lib

// using namespace lib;
#line 4 "utility/modint.hpp"

namespace lib {

template <ll m> struct modint {
    using mint = modint;
    ll a;

    modint(ll x = 0) : a((x % m + m) % m) {}
    static constexpr ll mod() {
        return m;
    }
    ll val() const {
        return a;
    }
    ll& val() {
        return a;
    }
    mint pow(ll n) const {
        mint res = 1;
        mint x = a;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }
    mint inv() const {
        return pow(m - 2);
    }
    mint& operator+=(const mint rhs) {
        a += rhs.a;
        if (a >= m) a -= m;
        return *this;
    }
    mint& operator-=(const mint rhs) {
        if (a < rhs.a) a += m;
        a -= rhs.a;
        return *this;
    }
    mint& operator*=(const mint rhs) {
        a = a * rhs.a % m;
        return *this;
    }
    mint& operator/=(mint rhs) {
        *this *= rhs.inv();
        return *this;
    }
    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const modint &lhs, const modint &rhs) {
        return lhs.a == rhs.a;
    }
    friend bool operator!=(const modint &lhs, const modint &rhs) {
        return !(lhs == rhs);
    }
    mint operator+() const {
        return *this;
    }
    mint operator-() const {
        return mint() - *this;
    }
};

using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1'000'000'007>;

}  // namespace lib
#line 4 "convolution/ntt4.hpp"

namespace lib {

// only for modint998244353
template<typename mint>
struct NTT {
    using uint = unsigned int;
    static constexpr uint mod = mint::mod();
    static constexpr ull mod2 = (ull)mod * mod;
    static constexpr uint pr  = 3; // for modint998244353
    static constexpr int level = 23; // for modint998244353
    array<mint,level+1> wp, wm;
    void set_ws(){
        mint r = mint(pr).pow((mod-1) >> level);
        wp[level] = r, wm[level] = r.inv();
        for (int i = level-1; i >= 0; i--){
            wp[i] = wp[i+1] * wp[i+1];
            wm[i] = wm[i+1] * wm[i+1];
        }
    }
    NTT () { set_ws(); }
    void fft4(vector<mint> &a, int k){
        uint im = wm[2].val();
        uint n = 1<<k;
        uint len = n;
        int d = k;
        while (len > 1){
            if (d == 1){
                for (int i = 0; i < (1<<(k-1)); i++){
                    a[i*2+0] += a[i*2+1];
                    a[i*2+1]  = a[i*2+0] - a[i*2+1] * 2;
                }
                len >>= 1;
                d -= 1;
            }
            else {
                int len4 = len/4;
                int nlen = n/len;
                ull r1 = 1, r2 = 1, r3 = 1, imr1 = im, imr3 = im;
                for (int i = 0; i < len4; i++){
                    for (int j = 0; j < nlen; j++){
                        uint a0 = a[len4*0+i + len*j].val();
                        uint a1 = a[len4*1+i + len*j].val();
                        uint a2 = a[len4*2+i + len*j].val();
                        uint a3 = a[len4*3+i + len*j].val();
                        uint a0p2 = a0 + a2;
                        uint a1p3 = a1 + a3;
                        ull b0m2 = (a0 + mod - a2) * r1;
                        ull b1m3 = (a1 + mod - a3) * imr1;
                        ull c0m2 = (a0 + mod - a2) * r3;
                        ull c1m3 = (a1 + mod - a3) * imr3;
                        a[len4*0+i + len*j] = a0p2 + a1p3;
                        a[len4*1+i + len*j] = b0m2 + b1m3;
                        a[len4*2+i + len*j] = (a0p2 + mod*2 - a1p3) * r2;
                        a[len4*3+i + len*j] = c0m2 + mod2*2 - c1m3;
                    }
                    r1 = r1 * wm[d].val() % mod;
                    r2 = r1 * r1 % mod;
                    r3 = r1 * r2 % mod;
                    imr1 = im * r1 % mod;
                    imr3 = im * r3 % mod;
                }
                len >>= 2;
                d -= 2;
            }
        }
    }
    void ifft4(vector<mint> &a, int k){
        uint im = wp[2].val();
        uint n = 1<<k;
        uint len = (k & 1 ? 2 : 4);
        int d = (k & 1 ? 1 : 2);
        while (len <= n){
            if (d == 1){
                for (int i = 0; i < (1<<(k-1)); i++){
                    a[i*2+0] += a[i*2+1];
                    a[i*2+1]  = a[i*2+0] - a[i*2+1] * 2;
                }
                len <<= 2;
                d += 2;
            }
            else {
                int len4 = len/4;
                int nlen = n/len;
                ull r1 = 1, r2 = 1, r3 = 1, imr1 = im, imr3 = im;
                for (int i = 0; i < len4; i++){
                    for (int j = 0; j < nlen; j++){
                        ull a0 = a[len4*0+i + len*j].val();
                        ull a1 = a[len4*1+i + len*j].val() * r1;
                        ull a2 = a[len4*2+i + len*j].val() * r2;
                        ull a3 = a[len4*3+i + len*j].val() * r3;
                        ull b1 = a[len4*1+i + len*j].val() * imr1;
                        ull b3 = a[len4*3+i + len*j].val() * imr3;
                        ull a0p2 = a0 + a2;
                        ull a1p3 = a1 + a3;
                        ull a0m2 = a0 + mod2 - a2;
                        ull b1m3 = b1 + mod2 - b3;
                        a[len4*0+i + len*j] = a0p2 + a1p3;
                        a[len4*1+i + len*j] = a0m2 + b1m3;
                        a[len4*2+i + len*j] = a0p2 + mod2*2 - a1p3;
                        a[len4*3+i + len*j] = a0m2 + mod2*2 - b1m3;
                    }
                    r1 = r1 * wp[d].val() % mod;
                    r2 = r1 * r1 % mod;
                    r3 = r1 * r2 % mod;
                    imr1 = im * r1 % mod;
                    imr3 = im * r3 % mod;
                }
                len <<= 2;
                d += 2;
            }
        }
    }
    vector<mint> multiply(const vector<mint> &a, const vector<mint> &b){
        if (a.empty() || b.empty()) return {};
        int d = a.size() + b.size() - 1;
        if (min<int>(a.size(), b.size()) <= 40){
            vector<mint> s(d);
            rep(i,0,a.size()) rep(j,0,b.size()) s[i+j] += a[i]*b[j];
            return s;
        }
        int k = 2, M = 4;
        while (M < d) M <<= 1, ++k;
        vector<mint> s(M), t(M);
        rep(i,0,a.size()) s[i] = a[i];
        rep(i,0,b.size()) t[i] = b[i];
        fft4(s,k);
        fft4(t,k);
        rep(i,0,M) s[i] *= t[i];
        ifft4(s, k);
        s.resize(d);
        mint invm = mint(M).inv();
        rep(i,0,d) s[i] *= invm;
        return s;
    }
};

} // namespace lib
#line 6 "fps/fps.hpp"

namespace lib {

template <class mint> struct FormalPowerSeries : std::vector<mint> {
  private:
    using FPS = FormalPowerSeries<mint>;
    using std::vector<mint>::vector;
    using std::vector<mint>::vector::operator=;

    NTT<mint> ntt;

  public:
    FormalPowerSeries(const std::vector<mint> &a) {
        *this = a;
    }

    FPS operator+(const FPS &rhs) const noexcept {
        return FPS(*this) += rhs;
    }
    FPS operator-(const FPS &rhs) const noexcept {
        return FPS(*this) -= rhs;
    }
    FPS operator*(const FPS &rhs) const noexcept {
        return FPS(*this) *= rhs;
    }
    FPS operator/(const FPS &rhs) const noexcept {
        return FPS(*this) /= rhs;
    }
    FPS operator%(const FPS &rhs) const noexcept {
        return FPS(*this) %= rhs;
    }

    FPS operator+(const mint &rhs) const noexcept {
        return FPS(*this) += rhs;
    }
    FPS operator-(const mint &rhs) const noexcept {
        return FPS(*this) -= rhs;
    }
    FPS operator*(const mint &rhs) const noexcept {
        return FPS(*this) *= rhs;
    }
    FPS operator/(const mint &rhs) const noexcept {
        return FPS(*this) /= rhs;
    }

    FPS &operator+=(const FPS &rhs) noexcept {
        if (this->size() < rhs.size()) this->resize(rhs.size());
        for (int i = 0; i < (int)rhs.size(); ++i) {
            (*this)[i] += rhs[i];
        }
        return *this;
    }

    FPS &operator-=(const FPS &rhs) noexcept {
        if (this->size() < rhs.size()) this->resize(rhs.size());
        for (int i = 0; i < (int)rhs.size(); ++i) {
            (*this)[i] -= rhs[i];
        }
        return *this;
    }

    FPS &operator*=(const FPS &rhs) noexcept {
        *this = ntt.multiply(*this, rhs);
        return *this;
    }

    FPS &operator/=(const FPS &rhs) noexcept {
        int n = deg() - 1;
        int m = rhs.deg() - 1;
        if (n < m) {
            *this = {};
            return *this;
        }
        *this = (*this).rev() * rhs.rev().inv(n - m + 1);
        (*this).resize(n - m + 1);
        std::reverse((*this).begin(), (*this).end());
        return *this;
    }

    FPS &operator%=(const FPS &rhs) noexcept {
        *this -= *this / rhs * rhs;
        shrink();
        return *this;
    }

    FPS &operator+=(const mint &rhs) noexcept {
        if (this->empty()) this->resize(1);
        (*this)[0] += rhs;
        return *this;
    }

    FPS &operator-=(const mint &rhs) noexcept {
        if (this->empty()) this->resize(1);
        (*this)[0] -= rhs;
        return *this;
    }

    FPS &operator*=(const mint &rhs) noexcept {
        for (int i = 0; i < deg(); ++i) {
            (*this)[i] *= rhs;
        }
        return *this;
    }
    FPS &operator/=(const mint &rhs) noexcept {
        mint inv_rhs = rhs.inv();
        for (int i = 0; i < deg(); ++i) {
            (*this)[i] *= inv_rhs;
        }
        return *this;
    }

    FPS operator>>(int d) const {
        if (deg() <= d) return {};
        FPS f = *this;
        f.erase(f.begin(), f.begin() + d);
        return f;
    }

    FPS operator<<(int d) const {
        FPS f = *this;
        f.insert(f.begin(), d, 0);
        return f;
    }

    FPS operator-() const {
        FPS g(this->size());
        for (int i = 0; i < (int)this->size(); i++) g[i] = -(*this)[i];
        return g;
    }

    FPS pre(int sz) const {
        return FPS(this->begin(), this->begin() + std::min(deg(), sz));
    }

    FPS rev() const {
        auto f = *this;
        std::reverse(f.begin(), f.end());
        return f;
    }

    FPS differential() const {
        int n = deg();
        FPS g(std::max(0, n - 1));
        for (int i = 0; i < n - 1; i++) {
            g[i] = (*this)[i + 1] * (i + 1);
        }
        return g;
    }

    FPS integral() const {
        int n = deg();
        FPS g(n + 1);
        g[0] = 0;
        if (n > 0) g[1] = 1;
        auto mod = mint::mod();
        for (int i = 2; i <= n; i++) g[i] = (-g[mod % i]) * (mod / i);
        for (int i = 0; i < n; i++) g[i + 1] *= (*this)[i];
        return g;
    }

    FPS inv(int d = -1) const {
        int n = 1;
        if (d < 0) d = deg();
        FPS g(n);
        g[0] = (*this)[0].inv();
        while (n < d) {
            n <<= 1;
            g = (g * 2 - g * g * this->pre(n)).pre(n);
        }
        g.resize(d);
        return g;
    }

    FPS log(int d = -1) const {
        assert((*this)[0].val() == 1);
        if (d < 0) d = deg();
        return ((*this).differential() * (*this).inv(d)).pre(d - 1).integral();
    }

    FPS exp(int d = -1) const {
        assert((*this)[0].val() == 0);
        int n = 1;
        if (d < 0) d = deg();
        FPS g(n);
        g[0] = 1;
        while (n < d) {
            n <<= 1;
            g = (g * (this->pre(n) - g.log(n) + 1)).pre(n);
        }
        g.resize(d);
        return g;
    }

    FPS pow(ll k, int d = -1) const {
        const int n = deg();
        if (d < 0) d = n;
        if (k == 0) {
            FPS f(d);
            if (d > 0) f[0] = 1;
            return f;
        }
        for (int i = 0; i < n; i++) {
            if ((*this)[i].val() != 0) {
                mint rev = (*this)[i].inv();
                FPS f = (((*this * rev) >> i).log(d) * k).exp(d);
                f *= (*this)[i].pow(k);
                f = (f << (i * k)).pre(d);
                if (f.deg() < d) f.resize(d);
                return f;
            }
            if (i + 1 >= (d + k - 1) / k) break;
        }
        return FPS(d);
    }

    int deg() const {
        return (*this).size();
    }

    void shrink() {
        while ((!this->empty()) && this->back() == 0) this->pop_back();
    }

    int count_terms() const {
        int c = 0;
        for (int i = 0; i < deg(); i++) {
            if ((*this)[i] != 0) c++;
        }
        return c;
    }
};

}  // namespace lib
#line 4 "fps/multipoint_evaluation.hpp"

namespace lib {

template<class mint>
std::vector<mint> multipoint_evaluation(FormalPowerSeries<mint> f, const std::vector<mint> &p) {
    using FPS = FormalPowerSeries<mint>;
    int m = 1;
    while (m < (int)p.size()) m <<= 1;
    std::vector<FPS> subproduct_tree(2 * m, {1});
    for (int i = 0; i < (int)p.size(); i++) {
        subproduct_tree[i + m] = FPS{-p[i], 1};
    }
    for (int i = m - 1; i >= 1; i--) {
        subproduct_tree[i] =
            subproduct_tree[2 * i] * subproduct_tree[2 * i + 1];
    }
    std::vector<FPS> subremainder_tree(2 * m);
    subremainder_tree[1] = f % subproduct_tree[1];
    for (int i = 2; i < m + (int)p.size(); i++) {
        if (subremainder_tree[i / 2].empty()) continue;
        subremainder_tree[i] = subremainder_tree[i / 2] % subproduct_tree[i];
    }
    std::vector<mint> fp(p.size());
    for (int i = 0; i < (int)p.size(); i++) {
        if (subremainder_tree[i + m].empty())
            fp[i] = 0;
        else
            fp[i] = subremainder_tree[i + m][0];
    }
    return fp;
}

}  // namespace ebi
#line 4 "test/polynomial/Multipoint_Evaluation.test.cpp"

#line 2 "convolution/ntt.hpp"

#line 5 "convolution/ntt.hpp"

namespace lib {

using mint = modint998244353;

struct ntt_info {
    static constexpr int rank2 = 23;
    const int g = 3;
    std::array<std::array<mint, rank2 + 1>, 2> root;

    ntt_info() {
        root[0][rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        root[1][rank2] = root[0][rank2].inv();
        rrep(i, 0, rank2) {
            root[0][i] = root[0][i + 1] * root[0][i + 1];
            root[1][i] = root[1][i + 1] * root[1][i + 1];
        }
    }
};

void butterfly(std::vector<mint>& a, bool inverse) {
    static ntt_info info;
    int n = a.size();
    int bit_size = 0;
    while ((1 << bit_size) < n) bit_size++;
    assert(1 << bit_size == n);
    for (int i = 0, j = 1; j < n - 1; j++) {
        for (int k = n >> 1; k > (i ^= k); k >>= 1);
        if (j < i) {
            std::swap(a[i], a[j]);
        }
    }
    rep(bit, 0, bit_size) {
        rep(i, 0, n / (1 << (bit + 1))) {
            mint zeta1 = 1;
            mint zeta2 = info.root[inverse][1];
            mint w = info.root[inverse][bit + 1];
            rep(j, 0, 1 << bit) {
                int idx = i * (1 << (bit + 1)) + j;
                int jdx = idx + (1 << bit);
                mint p1 = a[idx];
                mint p2 = a[jdx];
                a[idx] = p1 + zeta1 * p2;
                a[jdx] = p1 + zeta2 * p2;
                zeta1 *= w;
                zeta2 *= w;
            }
        }
    }
    if (inverse) {
        mint inv_n = mint(n).inv();
        rep(i, 0, n) a[i] *= inv_n;
    }
}

std::vector<mint> convolution(const std::vector<mint>& f,
                              const std::vector<mint>& g) {
    int n = 1;
    while (n < int(f.size() + g.size() - 1)) n <<= 1;
    std::vector<mint> a(n), b(n);
    std::copy(f.begin(), f.end(), a.begin());
    std::copy(g.begin(), g.end(), b.begin());
    butterfly(a, false);
    butterfly(b, false);
    rep(i, 0, n) {
        a[i] *= b[i];
    }
    butterfly(a, true);
    a.resize(f.size() + g.size() - 1);
    return a;
}

}  // namespace lib
#line 9 "test/polynomial/Multipoint_Evaluation.test.cpp"

namespace lib {

using mint = modint998244353;
using FPS = FormalPowerSeries<mint>;

void main_() {
    int n, m;
    std::cin >> n >> m;
    FPS f(n);
    rep(i,0,n) std::cin >> f[i].val();
    std::vector<mint> p(m);
    rep(i,0,m) std::cin >> p[i].val();
    auto fp = multipoint_evaluation<mint>(f, p);
    rep(i,0,m) {
        std::cout << fp[i].val() << " \n"[i == m-1];
    }
}

}  // namespace ebi

int main() {
    int t = 1;
    // std::cin >> t;
    while (t--) {
        lib::main_();
    }
    return 0;
}
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