結果

問題 No.931 Multiplicative Convolution
ユーザー satashunsatashun
提出日時 2020-04-20 21:18:40
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 151 ms / 2,000 ms
コード長 6,743 bytes
コンパイル時間 2,589 ms
コンパイル使用メモリ 203,560 KB
最終ジャッジ日時 2025-01-09 22:01:11
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 14
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define ALL(c) (c).begin(), (c).end()

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U>
void chmin(T& t, const U& u) {
    if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
    if (t < u) t = u;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << "," << p.second << ")";
    return os;
}

template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    rep(i, v.size()) {
        if (i) os << ",";
        os << v[i];
    }
    os << "}";
    return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << H;
    debug_out(T...);
}
#define debug(...) \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

template <unsigned int MOD>
struct ModInt {
    using uint = unsigned int;
    using ull = unsigned long long;
    using M = ModInt;

    uint v;

    ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
    M& set_norm(uint _v) {  //[0, MOD * 2)->[0, MOD)
        v = (_v < MOD) ? _v : _v - MOD;
        return *this;
    }

    explicit operator bool() const { return v != 0; }
    M operator+(const M& a) const { return M().set_norm(v + a.v); }
    M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
    M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
    M operator/(const M& a) const { return *this * a.inv(); }
    M& operator+=(const M& a) { return *this = *this + a; }
    M& operator-=(const M& a) { return *this = *this - a; }
    M& operator*=(const M& a) { return *this = *this * a; }
    M& operator/=(const M& a) { return *this = *this / a; }
    M operator-() const { return M() - *this; }
    M& operator++(int) { return *this = *this + 1; }
    M& operator--(int) { return *this = *this - 1; }

    M pow(ll n) const {
        if (n < 0) return inv().pow(-n);
        M x = *this, res = 1;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }

    M inv() const {
        ll a = v, b = MOD, p = 1, q = 0, t;
        while (b != 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(p -= t * q, q);
        }
        return M(p);
    }

    bool operator==(const M& a) const { return v == a.v; }
    bool operator!=(const M& a) const { return v != a.v; }
    friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
    static int get_mod() { return MOD; }
};

using Mint = ModInt<998244353>;

// depend on ModInt, must use NTT friendly mod

template <class D>
struct NumberTheoreticTransform {
    D root;
    V<D> roots = {0, 1};
    V<int> rev = {0, 1};
    int base = 1, max_base = -1;

    void init() {
        int mod = D::get_mod();
        int tmp = mod - 1;
        max_base = 0;
        while (tmp % 2 == 0) {
            tmp /= 2;
            max_base++;
        }

        root = 2;

        while (true) {
            if (root.pow(1 << max_base).v == 1) {
                if (root.pow(1 << (max_base - 1)).v != 1) {
                    break;
                }
            }
            root++;
        }
    }

    void ensure_base(int nbase) {
        if (max_base == -1) init();
        if (nbase <= base) return;
        assert(nbase <= max_base);

        rev.resize(1 << nbase);
        for (int i = 0; i < (1 << nbase); ++i) {
            rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
        }
        roots.resize(1 << nbase);

        while (base < nbase) {
            D z = root.pow(1 << (max_base - 1 - base));
            for (int i = 1 << (base - 1); i < (1 << base); ++i) {
                roots[i << 1] = roots[i];
                roots[(i << 1) + 1] = roots[i] * z;
            }
            ++base;
        }
    }

    void ntt(V<D>& a, bool inv = false) {
        int n = a.size();
        // assert((n & (n - 1)) == 0);
        int zeros = __builtin_ctz(n);
        ensure_base(zeros);
        int shift = base - zeros;

        for (int i = 0; i < n; i++) {
            if (i < (rev[i] >> shift)) {
                swap(a[i], a[rev[i] >> shift]);
            }
        }

        for (int k = 1; k < n; k <<= 1) {
            for (int i = 0; i < n; i += 2 * k) {
                for (int j = 0; j < k; j++) {
                    D x = a[i + j];
                    D y = a[i + j + k] * roots[j + k];
                    a[i + j] = x + y;
                    a[i + j + k] = x - y;
                }
            }
        }

        int v = D(n).inv().v;
        if (inv) {
            reverse(a.begin() + 1, a.end());
            for (int i = 0; i < n; i++) {
                a[i] *= v;
            }
        }
    }

    V<D> mul(V<D> a, V<D> b) {
        int s = a.size() + b.size() - 1;
        int nbase = 1;
        while ((1 << nbase) < s) nbase++;
        int sz = 1 << nbase;
        a.resize(sz);
        b.resize(sz);
        ntt(a);
        ntt(b);

        for (int i = 0; i < sz; i++) {
            a[i] *= b[i];
        }
        ntt(a, true);

        a.resize(s);
        return a;
    }
};

int main() {
    NumberTheoreticTransform<Mint> ntt;
    ntt.init();

    int P;
    cin >> P;
    V<int> A(P), B(P);
    for (int i = 1; i < P; ++i) cin >> A[i];
    for (int i = 1; i < P; ++i) cin >> B[i];

    int g = 1;
    {
        while (true) {
            ll t = 1;
            int ord = 0;
            while (true) {
                t = t * g % P;
                ++ord;
                if (t == 1) {
                    break;
                }
            }
            if (ord == P - 1) {
                break;
            }
            ++g;
        }
    }

    V<Mint> va(P - 1), vb(P - 1);
    int x = 1;

    rep(i, P - 1) {
        va[i] = A[x];
        vb[i] = B[x];
        x = (ll)x * g % P;
    }

    auto vec = ntt.mul(va, vb);
    rep(i, vec.size()) if (i >= P - 1) { vec[i - (P - 1)] += vec[i]; }
    V<Mint> ans(P);
    x = 1;
    rep(i, P - 1) {
        ans[x] = vec[i];
        x = (ll)x * g % P;
    }
    rep(i, P) if (i) { cout << ans[i] << (i == P - 1 ? '\n' : ' '); }
    return 0;
}
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