結果
| 問題 | No.2349 Power!! (Hard) |
| コンテスト | |
| ユーザー |
 hos.lyric
|
| 提出日時 | 2023-06-09 22:02:07 |
| 言語 | C++14 (gcc 15.2.0 + boost 1.89.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 7,075 bytes |
| 記録 | |
| コンパイル時間 | 2,970 ms |
| コンパイル使用メモリ | 194,168 KB |
| 実行使用メモリ | 6,400 KB |
| 最終ジャッジ日時 | 2026-06-05 20:16:56 |
| 合計ジャッジ時間 | 61,854 ms |
|
ジャッジサーバーID （参考情報） |
judge3_1 / judge2_0 |
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| ファイルパターン | 結果 |
|---|---|
| sample | WA * 1 |
| other | WA * 10 TLE * 2 |
ソースコード
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("avx2")
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;
#include "atcoder/convolution"
void fft(vector<Mint> &as) {
using mint = atcoder::modint998244353;
vector<mint> as_(as.size());
for (int i = 0; i < (int)as.size(); ++i) as_[i] = mint::raw(as[i].x);
atcoder::internal::butterfly(as_);
for (int i = 0; i < (int)as.size(); ++i) as[i].x = as_[i].val();
}
void invFft(vector<Mint> &as) {
using mint = atcoder::modint998244353;
vector<mint> as_(as.size());
for (int i = 0; i < (int)as.size(); ++i) as_[i] = mint::raw(as[i].x);
atcoder::internal::butterfly_inv(as_);
for (int i = 0; i < (int)as.size(); ++i) as[i].x = as_[i].val();
}
/*
[0, n] * [0, n - m + 1]
[ a[0] ]
[ ... a[0] ]
[ a[m-1] ... ]
[ a[m-1] ]
[ ... ]
[ a[0] ]
[ ... ]
[ a[m-1] ]
[x^j] (rev(a) b) m - 1 <= j <= n - 1
*/
vector<Mint> middle(vector<Mint> as, vector<Mint> bs) {
const int m = as.size();
const int n = bs.size();
assert(m <= n);
int nn = 1;
for (; nn < n; nn <<= 1) {}
reverse(as.begin(), as.end());
as.resize(nn, 0);
fft(as);
bs.resize(nn, 0);
fft(bs);
for (int i = 0; i < nn; ++i) {
bs[i] *= as[i];
}
invFft(bs);
bs.resize(n);
bs.erase(bs.begin(), bs.begin() + (m - 1));
return bs;
}
// a^e, 0 <= e < 2^32
struct Power {
static constexpr int E = 11;
vector<Mint> baby, mid, giant;
Power() {}
Power(Mint a) : baby((1 << E) + 1), mid((1 << E) + 1), giant(1 << E) {
baby[0] = 1;
for (int i = 1; i <= 1 << E; ++i) baby[i] = baby[i - 1] * a;
mid[0] = 1;
for (int i = 1; i <= 1 << E; ++i) mid[i] = mid[i - 1] * baby[1 << E];
giant[0] = 1;
for (int i = 1; i < 1 << E; ++i) giant[i] = giant[i - 1] * mid[1 << E];
}
Mint operator()(unsigned e) const {
return baby[e & ((1<<E)-1)] * mid[(e >> E) & ((1<<E)-1)] * giant[e >> (2*E)];
}
};
int main() {
for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
Mint A;
int N;
scanf("%u%d", &A.x, &N);
const int K = sqrt(N);
const Power aa(A);
const Power aaKK(aa(K * K));
vector<Mint> as(K);
for (int j = 0; j < K; ++j) {
as[j] = aa(j * j);
}
// cerr<<"as = "<<as<<endl;
const Mint B = aa(2 * K);
const Mint invB = B.inv();
vector<Mint> bb2(2 * K);
{
Mint bb = 1;
bb2[0] = 1;
for (int i = 1; i < 2 * K; ++i) {
bb2[i] = bb2[i - 1] * bb;
bb *= B;
}
}
vector<Mint> invbb2(K);
{
Mint invbb = 1;
invbb2[0] = 1;
for (int i = 1; i < K; ++i) {
invbb2[i] = invbb2[i - 1] * invbb;
invbb *= invB;
}
}
auto gs = as;
for (int i = 0; i < K; ++i) {
gs[i] *= invbb2[i];
}
auto fs = middle(gs, bb2);
for (int i = 0; i < K; ++i) {
fs[i] *= invbb2[i];
}
// cerr<<"fs = "<<fs<<endl;
Mint ans = 0;
for (int i = 0; i < K; ++i) {
ans += aaKK(i * i) * fs[i];
}
{
Mint pw = aaKK(K * K);
for (int i = K * K; i < N; ++i) {
ans += pw;
pw *= aa(2 * i + 1);
}
}
printf("%u\n", ans.x);
}
#ifndef LOCAL
break;
#endif
}
return 0;
}