結果
| 問題 |
No.2679 MODice
|
| コンテスト | |
| ユーザー |
 shinchan
|
| 提出日時 | 2024-03-20 21:03:46 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 10,733 bytes |
| コンパイル時間 | 2,893 ms |
| コンパイル使用メモリ | 218,008 KB |
| 最終ジャッジ日時 | 2025-02-20 08:20:17 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 5 TLE * 1 -- * 9 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#define all(v) (v).begin(),(v).end()
#define pb(a) push_back(a)
#define rep(i, n) for(int i=0;i<n;i++)
#define foa(e, v) for(auto&& e : v)
using ll = long long;
const ll MOD7 = 1000000007, MOD998 = 998244353, INF = (1LL << 60);
#define dout(a) cout<<fixed<<setprecision(10)<<a<<endl;
template<int MOD> struct Modint {
long long val;
constexpr Modint(long long v = 0) noexcept : val(v % MOD) { if (val < 0) val += MOD; }
constexpr int mod() const { return MOD; }
constexpr long long value() const { return val; }
constexpr Modint operator - () const noexcept { return val ? MOD - val : 0; }
constexpr Modint operator + (const Modint& r) const noexcept { return Modint(*this) += r; }
constexpr Modint operator - (const Modint& r) const noexcept { return Modint(*this) -= r; }
constexpr Modint operator * (const Modint& r) const noexcept { return Modint(*this) *= r; }
constexpr Modint operator / (const Modint& r) const noexcept { return Modint(*this) /= r; }
constexpr Modint& operator += (const Modint& r) noexcept {
val += r.val;
if (val >= MOD) val -= MOD;
return *this;
}
constexpr Modint& operator -= (const Modint& r) noexcept {
val -= r.val;
if (val < 0) val += MOD;
return *this;
}
constexpr Modint& operator *= (const Modint& r) noexcept {
val = val * r.val % MOD;
return *this;
}
constexpr Modint& operator /= (const Modint& r) noexcept {
long long a = r.val, b = MOD, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
val = val * u % MOD;
if (val < 0) val += MOD;
return *this;
}
constexpr bool operator == (const Modint& r) const noexcept { return this->val == r.val; }
constexpr bool operator != (const Modint& r) const noexcept { return this->val != r.val; }
friend constexpr istream& operator >> (istream& is, Modint<MOD>& x) noexcept {
is >> x.val;
x.val %= MOD;
if (x.val < 0) x.val += MOD;
return is;
}
friend constexpr ostream& operator << (ostream& os, const Modint<MOD>& x) noexcept {
return os << x.val;
}
constexpr Modint<MOD> pow(long long n) noexcept {
if (n == 0) return 1;
if (n < 0) return this->pow(-n).inv();
Modint<MOD> ret = pow(n >> 1);
ret *= ret;
if (n & 1) ret *= *this;
return ret;
}
constexpr Modint<MOD> inv() noexcept {
long long a = this->val, b = MOD, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
return Modint<MOD>(u);
}
};
const int MOD = MOD998;
using mint = Modint<MOD>;
long long modinv(long long a, long long MOD) {
long long b = MOD, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b; std::swap(a, b);
u -= t * v; std::swap(u, v);
}
u %= MOD;
if (u < 0) u += MOD;
return u;
}
long long modpow(long long a, long long n, long long MOD) {
long long res = 1;
a %= MOD;
if(n < 0) {
n = -n;
a = modinv(a, MOD);
}
while (n > 0) {
if (n & 1) res = res * a % MOD;
a = a * a % MOD;
n >>= 1;
}
return res;
}
namespace NTT {
int calc_primitive_root(int MOD) {
if (MOD == 2) return 1;
if (MOD == 167772161) return 3;
if (MOD == 469762049) return 3;
if (MOD == 754974721) return 11;
if (MOD == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
long long x = (MOD - 1) >> 1;
while (x % 2 == 0) x >>= 1;
for (long long i = 3; i * i <= x; i += 2) {
if (x % i == 0) {
divs[cnt ++] = i;
while (x % i == 0) x /= i;
}
}
if (x > 1) divs[cnt++] = x;
for (int g = 2;; ++ g) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (modpow(g, (MOD - 1) / divs[i], MOD) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
int get_fft_size(int N, int M) {
int size_a = 1, size_b = 1;
while (size_a < N) size_a <<= 1;
while (size_b < M) size_b <<= 1;
return std::max(size_a, size_b) << 1;
}
template<class mint> void trans(std::vector<mint>& v, bool inv = false) {
if (v.empty()) return;
int N = (int) v.size();
int MOD = v[0].mod();
int PR = calc_primitive_root(MOD);
static bool first = true;
static std::vector<long long> vbw(30), vibw(30);
if (first) {
first = false;
for (int k = 0; k < 30; ++ k) {
vbw[k] = modpow(PR, (MOD - 1) >> (k + 1), MOD);
vibw[k] = modinv(vbw[k], MOD);
}
}
for (int i = 0, j = 1; j < N - 1; ++ j) {
for (int k = N >> 1; k > (i ^= k); k >>= 1);
if (i > j) std::swap(v[i], v[j]);
}
for (int k = 0, t = 2; t <= N; ++ k, t <<= 1) {
long long bw = vbw[k];
if (inv) bw = vibw[k];
for (int i = 0; i < N; i += t) {
mint w = 1;
for (int j = 0; j < (t >> 1); ++ j) {
int j1 = i + j, j2 = i + j + (t >> 1);
mint c1 = v[j1], c2 = v[j2] * w;
v[j1] = c1 + c2;
v[j2] = c1 - c2;
w *= bw;
}
}
}
if (inv) {
long long invN = modinv(N, MOD);
for (int i = 0; i < N; ++ i) v[i] = v[i] * invN;
}
}
static constexpr int MOD0 = 754974721;
static constexpr int MOD1 = 167772161;
static constexpr int MOD2 = 469762049;
using mint0 = Modint<MOD0>;
using mint1 = Modint<MOD1>;
using mint2 = Modint<MOD2>;
static const mint1 imod0 = 95869806; // modinv(MOD0, MOD1);
static const mint2 imod1 = 104391568; // modinv(MOD1, MOD2);
static const mint2 imod01 = 187290749; // imod1 / MOD0;
// small case (T = mint, long long)
template<class T> std::vector<T> naive_mul
(const std::vector<T>& A, const std::vector<T>& B) {
if (A.empty() || B.empty()) return {};
int N = (int) A.size(), M = (int) B.size();
std::vector<T> res(N + M - 1);
for (int i = 0; i < N; ++ i)
for (int j = 0; j < M; ++ j)
res[i + j] += A[i] * B[j];
return res;
}
};
// mint
template<class mint> std::vector<mint> convolution
(const std::vector<mint>& A, const std::vector<mint>& B) {
if (A.empty() || B.empty()) return {};
int N = (int) A.size(), M = (int) B.size();
if (std::min(N, M) < 30) return NTT::naive_mul(A, B);
int MOD = A[0].mod();
int size_fft = NTT::get_fft_size(N, M);
if (MOD == 998244353) {
std::vector<mint> a(size_fft), b(size_fft), c(size_fft);
for (int i = 0; i < N; ++i) a[i] = A[i];
for (int i = 0; i < M; ++i) b[i] = B[i];
NTT::trans(a), NTT::trans(b);
std::vector<mint> res(size_fft);
for (int i = 0; i < size_fft; ++i) res[i] = a[i] * b[i];
NTT::trans(res, true);
res.resize(N + M - 1);
return res;
}
std::vector<NTT::mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
std::vector<NTT::mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
std::vector<NTT::mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
for (int i = 0; i < N; ++ i) {
a0[i] = A[i].value();
a1[i] = A[i].value();
a2[i] = A[i].value();
}
for (int i = 0; i < M; ++ i) {
b0[i] = B[i].value();
b1[i] = B[i].value();
b2[i] = B[i].value();
}
NTT::trans(a0), NTT::trans(a1), NTT::trans(a2),
NTT::trans(b0), NTT::trans(b1), NTT::trans(b2);
for (int i = 0; i < size_fft; ++i) {
c0[i] = a0[i] * b0[i];
c1[i] = a1[i] * b1[i];
c2[i] = a2[i] * b2[i];
}
NTT::trans(c0, true), NTT::trans(c1, true), NTT::trans(c2, true);
static const mint mod0 = NTT::MOD0, mod01 = mod0 * NTT::MOD1;
std::vector<mint> res(N + M - 1);
for (int i = 0; i < N + M - 1; ++ i) {
int y0 = c0[i].value();
int y1 = (NTT::imod0 * (c1[i] - y0)).value();
int y2 = (NTT::imod01 * (c2[i] - y0) - NTT::imod1 * y1).value();
res[i] = mod01 * y2 + mod0 * y1 + y0;
}
return res;
}
// long long
std::vector<long long> convolution_ll
(const std::vector<long long>& A, const std::vector<long long>& B) {
if (A.empty() || B.empty()) return {};
int N = (int) A.size(), M = (int) B.size();
if (std::min(N, M) < 30) return NTT::naive_mul(A, B);
int size_fft = NTT::get_fft_size(N, M);
std::vector<NTT::mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
std::vector<NTT::mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
std::vector<NTT::mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
for (int i = 0; i < N; ++ i) {
a0[i] = A[i];
a1[i] = A[i];
a2[i] = A[i];
}
for (int i = 0; i < M; ++ i) {
b0[i] = B[i];
b1[i] = B[i];
b2[i] = B[i];
}
NTT::trans(a0), NTT::trans(a1), NTT::trans(a2),
NTT::trans(b0), NTT::trans(b1), NTT::trans(b2);
for (int i = 0; i < size_fft; ++ i) {
c0[i] = a0[i] * b0[i];
c1[i] = a1[i] * b1[i];
c2[i] = a2[i] * b2[i];
}
NTT::trans(c0, true), NTT::trans(c1, true), NTT::trans(c2, true);
static const long long mod0 = NTT::MOD0, mod01 = mod0 * NTT::MOD1;
static const __int128_t mod012 = (__int128_t)mod01 * NTT::MOD2;
std::vector<long long> res(N + M - 1);
for (int i = 0; i < N + M - 1; ++ i) {
int y0 = c0[i].value();
int y1 = (NTT::imod0 * (c1[i] - y0)).value();
int y2 = (NTT::imod01 * (c2[i] - y0) - NTT::imod1 * y1).value();
__int128_t tmp = (__int128_t)mod01 * y2 + (__int128_t)mod0 * y1 + y0;
if(tmp < (mod012 >> 1)) res[i] = tmp;
else res[i] = tmp - mod012;
}
return res;
}
// depends on {modint.cpp}
int main() {
cin.tie(0);
ios::sync_with_stdio(false);
ll n, k;
cin >> n >> k;
vector<mint> a(6, 0);
a[0] = 1;
rep(i, n) {
vector<mint> b(6, 1);
a = convolution(a, b);
for(int j = 6; j <= 10; j ++) a[j - 6] += a[j];
a.resize(6);
}
cout << a[k] / mint(6).pow(n) << endl;
return 0;
}