結果

問題 No.2506 Sum of Weighted Powers
ユーザー suisen
提出日時 2023-03-22 01:29:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
(最新)
AC  
(最初)
実行時間 -
コード長 4,477 bytes
コンパイル時間 2,627 ms
コンパイル使用メモリ 142,148 KB
最終ジャッジ日時 2025-02-11 16:01:22
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
other AC * 5 WA * 37
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ソースコード

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プレゼンテーションモードにする

#include <iostream>
#include <cassert>
#include <cmath>
#include <map>
long long pow(long long a, long long n, long long p) {
    long long r = 1;
    for (;n > 0;n >>= 1, a = a * a % p)if (n % 2 == 1)r = r * a % p;
    return r;
}
int cnt(long long a, long long base, long long p) {
    int ret = 0;
    while (a != 1) {
        a = pow(a, base, p);
        ++ret;
    }
    return ret;
}
long long inv(long long a, long long p) {
    a %= p;
    long long u = 1, v = 0;
    long long b = p;
    while (b > 0) {
        long long q = a / b;
        a %= b;
        u -= v * q % p;
        u = (u % p + p) % p;
        {
            u ^= v;v ^= u;u ^= v;
            a ^= b;b ^= a;a ^= b;
        }
    }
    return u < 0 ? u + p : u;
}
long long gcd(long long a, long long b) {
    return a == 0 ? b : gcd(b % a, a);
}
long long peth_root(long long a, long long p, int e, long long mod) {
    long long q = mod - 1;
    int s = 0;
    while (q % p == 0) {
        q /= p;
        ++s;
    }
    long long pe = pow(p, e, mod);
    long long ans = pow(a, ((pe - 1) * inv(q, pe) % pe * q + 1) / pe, mod);
    long long c = 2;
    while (pow(c, (mod - 1) / p, mod) == 1)
        ++c;
    c = pow(c, q, mod);
    std::map<long long, int> map;
    long long add = 1;
    int v = (int) std::sqrt((double) (s - e) * p) + 1;
    long long mul = pow(c, v * pow(p, s - 1, mod - 1) % (mod - 1), mod);
    for (int i = 0;i <= v;++i) {
        map[add] = i;
        add = add * mul % mod;
    }
    mul = inv(pow(c, pow(p, s - 1, mod - 1), mod), mod);
    for (int i = e;i < s;++i) {
        long long err = inv(pow(ans, pe, mod), mod) * a % mod;
        long long target = pow(err, pow(p, s - 1 - i, mod - 1), mod);
        for (int j = 0; j <= v; ++j) {
            if (map.find(target) != map.end()) {
                int x = map[target];
                ans = ans * pow(c, (j + v * x) * pow(p, i - e, mod - 1) % (mod - 1), mod) % mod;
                break;
            }
            target = target * mul % mod;
            assert(j != v);
        }
    }
    return ans;
}
long long kth_root(long long a, long long k, long long p) {
    if (k > 0 && a == 0)return 0;
    k %= p - 1;
    long long g = gcd(k, p - 1);
    if (pow(a, (p - 1) / g, p) != 1)
        return -1;
    a = pow(a, inv(k / g, (p - 1) / g), p);
    for (long long div = 2;div * div <= g;++div) {
        int sz = 0;
        while (g % div == 0) {
            g /= div;
            ++sz;
        }
        if (sz > 0) {
            long long b = peth_root(a, div, sz, p);
            a = b;
        }
    }
    if (g > 1)
        a = peth_root(a, g, 1, p);
    return a;
}
#include <atcoder/modint>
using mint = atcoder::modint998244353;
namespace atcoder {
    std::istream& operator>>(std::istream& in, mint &a) {
        long long e; in >> e; a = e;
        return in;
    }
    
    std::ostream& operator<<(std::ostream& out, const mint &a) {
        out << a.val();
        return out;
    }
} // namespace atcoder
#include <atcoder/convolution>
mint solve(const int n, const mint x, const std::vector<mint> &a, const std::vector<mint> &b, const std::vector<mint> &c) {
    if (x == 0) {
        mint ans = 0;
        for (int i = 0; i <= n; ++i) {
            ans += a[i] * b[i] * c[0];
        }
        for (int i = 1; i <= n; ++i) {
            ans += a[i] * b[0] * c[i];
        }
        return ans;
    }
    int cbrt_x_ = kth_root(x.val(), 3, mint::mod());
    if (cbrt_x_ == -1) {
        return 0;
    }
    const mint cbrt_x = cbrt_x_, inv_cbrt_x = cbrt_x.inv();
    auto t = [&](long long k) {
        return k * k * k;
    };
    std::vector<mint> f(n + 1), g(n + 1);
    for (int i = 0; i <= n; ++i) {
        const mint pow_inv_x = inv_cbrt_x.pow(t(i));
        f[i] = b[i] * pow_inv_x;
        g[i] = c[i] * pow_inv_x;
    }
    const std::vector<mint> h = atcoder::convolution(f, g);
    mint ans = 0;
    for (int i = 0; i <= n; ++i) {
        const mint pow_x = cbrt_x.pow(t(i));
        ans += a[i] * pow_x * h[i];
    }
    return ans;
}
int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int n, x;
    std::cin >> n >> x;
    
    std::vector<mint> a(n + 1), b(n + 1), c(n + 1);
    for (int i = 0, v; i <= n; ++i) std::cin >> v, a[i] = v;
    for (int i = 0, v; i <= n; ++i) std::cin >> v, b[i] = v;
    for (int i = 0, v; i <= n; ++i) std::cin >> v, c[i] = v;
    std::cout << solve(n, x, a, b, c).val() << std::endl;
    return 0;
}
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