結果

問題 No.2349 Power!! (Hard)
コンテスト
ユーザー Forested
提出日時 2023-06-05 21:38:38
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3,662 ms / 7,000 ms
コード長 5,536 bytes
コンパイル時間 3,173 ms
コンパイル使用メモリ 164,080 KB
最終ジャッジ日時 2025-02-13 22:57:40
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 12
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 # 

#ifndef LOCAL
#define FAST_IO
#endif

// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

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

#ifdef INT128

using u128 = __uint128_t;
using i128 = __int128_t;

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64)x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64)x;
    return os;
}

#endif

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
// ============

#ifdef DEBUGF
#else
#define DBG(x) (void) 0
#endif

// ============

// ============

#include <algorithm>
#include <iostream>
#include <atcoder/convolution>

namespace poly {

using Mint = atcoder::modint998244353;
using Poly = std::vector<Mint>;

Poly add(Poly f, Poly g) {
    if (f.size() < g.size()) {
        std::swap(f, g);
    }
    for (int i = 0; i < (int)g.size(); ++i) {
        f[i] += g[i];
    }
    return f;
}

Poly sub(Poly f, Poly g) {
    if (f.size() < g.size()) {
        std::swap(f, g);
    }
    for (int i = 0; i < (int)g.size(); ++i) {
        f[i] -= g[i];
    }
    return f;
}

Poly mul(const Poly &f, const Poly &g) {
    return atcoder::convolution(f, g);
}

void dft(Poly &f) {
    atcoder::internal::butterfly(f);
}

void idft(Poly &f) {
    atcoder::internal::butterfly_inv(f);
    Mint inv = Mint::raw(f.size()).inv();
    for (Mint &cf : f) {
        cf *= inv;
    }
}

} // namespace poly
// ============

namespace poly {

std::vector<Mint> geometric_multipoint_evaluation(const Poly &f, int m, Mint a, Mint r) {
    int n = (int)f.size();
    if (n == 0) {
        return std::vector<Mint>(m, Mint());
    }
    if (m == 0) {
        return std::vector<Mint>();
    }
    if (r == Mint()) {
        Mint ev;
        Mint p(1);
        for (int i = 0; i < n; ++i) {
            ev += f[i] * p;
            p *= a;
        }
        std::vector<Mint> ret(m, f[0]);
        ret[0] = ev;
        return ret;
    }
    std::vector<Mint> w(n + m - 1), w_inv(std::max(n, m));
    {
        Mint v(1), pw(1);
        for (int i = 0; i < n + m - 1; ++i) {
            w[i] = v;
            v *= pw;
            pw *= r;
        }
    }
    {
        Mint inv = r.inv();
        Mint v(1), pw(1);
        for (int i = 0; i < std::max(n, m); ++i) {
            w_inv[i] = v;
            v *= pw;
            pw *= inv;
        }
    }
    std::vector<Mint> y(n);
    {
        Mint pw(1);
        for (int i = 0; i < n; ++i) {
            y[i] = f[i] * pw * w_inv[i];
            pw *= a;
        }
    }
    std::reverse(y.begin(), y.end());
    std::vector<Mint> conv = mul(y, w);
    std::vector<Mint> ans(conv.begin() + (n - 1), conv.begin() + (n + m - 1));
    for (int i = 0; i < m; ++i) {
        ans[i] *= w_inv[i];
    }
    return ans;
}

} // namespace poly
// ============

using poly::Mint;

constexpr u32 P = 998244353;
constexpr u32 D = 1 << 20;
constexpr u32 E = P / D;

Vec<Mint> mod_e(Mint a, i32 n) {
    i32 m = n / E;
    poly::Poly g(m);
    REP(i, m) {
        g[i] = a.pow((i64)E * E * i * i);
    }
    Vec<Mint> ans = poly::geometric_multipoint_evaluation(g, E, Mint::raw(1), a.pow(2 * E));
    REP(i, E) {
        ans[i] *= a.pow((i64)i * i);
    }
    REP(i, m * E, n) {
        ans[i % E] += a.pow((i64)i * i);
    }
    return ans;
}

Mint part_1(Mint a, i32 l) {
    poly::Poly f(l);
    REP(i, l) {
        f[i] = a.pow((i64)D * D * i * i);
    }
    Vec<Mint> gme = poly::geometric_multipoint_evaluation(f, E, Mint::raw(1), a.pow(2 * D));
    Vec<Mint> moe = mod_e(a, D);
    Mint ans;
    REP(i, E) {
        ans += gme[i] * moe[i];
    }
    return ans;
}

Mint part_2(Mint a, i32 l, i32 r) {
    Vec<Mint> moe = mod_e(a, r);
    Mint ans;
    REP(i, E) {
        ans += a.pow((i64)2 * l * D * i) * moe[i];
    }
    ans *= a.pow((i64)l * l * D * D);
    return ans;
}

Mint solve(Mint a, i32 n) {
    return part_1(a, n / D) + part_2(a, n / D, n % D);
}

int main() {
    i32 t;
    cin >> t;
    while (t--) {
        i32 a, n;
        cin >> a >> n;
        cout << solve(Mint::raw(a), n).val() << '\n';
    }
}
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