結果
| 問題 | No.213 素数サイコロと合成数サイコロ (3-Easy) |
| ユーザー |
 shinchan
|
| 提出日時 | 2023-01-27 13:45:59 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,011 ms / 3,000 ms |
| コード長 | 20,082 bytes |
| コンパイル時間 | 3,063 ms |
| コンパイル使用メモリ | 233,896 KB |
| 実行使用メモリ | 6,940 KB |
| 最終ジャッジ日時 | 2024-06-28 00:39:44 |
| 合計ジャッジ時間 | 5,916 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 688 ms
6,812 KB |
| testcase_01 | AC | 1,011 ms
6,940 KB |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl
template<class T1, class T2> ostream& operator << (ostream &s, pair<T1,T2> P)
{ return s << '<' << P.first << ", " << P.second << '>'; }
template<class T> ostream& operator << (ostream &s, vector<T> P)
{ for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; }
template<class T> ostream& operator << (ostream &s, vector<vector<T> > P)
{ for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl; }
template<class T> ostream& operator << (ostream &s, set<T> P)
{ for(auto it : P) { s << "<" << it << "> "; } return s << endl; }
template<class T1, class T2> ostream& operator << (ostream &s, map<T1,T2> P)
{ for(auto it : P) { s << "<" << it.first << "->" << it.second << "> "; } return s << endl; }
// modint
template<int MOD> struct Fp {
long long val;
constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
if (val < 0) val += MOD;
}
constexpr int getmod() const { return MOD; }
constexpr Fp operator - () const noexcept {
return val ? MOD - val : 0;
}
constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
constexpr Fp& operator += (const Fp& r) noexcept {
val += r.val;
if (val >= MOD) val -= MOD;
return *this;
}
constexpr Fp& operator -= (const Fp& r) noexcept {
val -= r.val;
if (val < 0) val += MOD;
return *this;
}
constexpr Fp& operator *= (const Fp& r) noexcept {
val = val * r.val % MOD;
return *this;
}
constexpr Fp& operator /= (const Fp& 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 Fp& r) const noexcept {
return this->val == r.val;
}
constexpr bool operator != (const Fp& r) const noexcept {
return this->val != r.val;
}
friend constexpr istream& operator >> (istream& is, Fp<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 Fp<MOD>& x) noexcept {
return os << x.val;
}
friend constexpr Fp<MOD> modpow(const Fp<MOD>& r, long long n) noexcept {
if (n == 0) return 1;
if (n < 0) return modpow(modinv(r), -n);
auto t = modpow(r, n / 2);
t = t * t;
if (n & 1) t = t * r;
return t;
}
friend constexpr Fp<MOD> modinv(const Fp<MOD>& 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);
}
return Fp<MOD>(u);
}
};
namespace NTT {
long long modpow(long long a, long long n, int mod) {
long long res = 1;
while (n > 0) {
if (n & 1) res = res * a % mod;
a = a * a % mod;
n >>= 1;
}
return res;
}
long long modinv(long long a, int mod) {
long long 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);
}
u %= mod;
if (u < 0) u += mod;
return u;
}
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) / 2;
while (x % 2 == 0) x /= 2;
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 max(size_a, size_b) << 1;
}
// number-theoretic transform
template<class mint> void trans(vector<mint>& v, bool inv = false) {
if (v.empty()) return;
int N = (int)v.size();
int MOD = v[0].getmod();
int PR = calc_primitive_root(MOD);
static bool first = true;
static 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) 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/2; ++j) {
int j1 = i + j, j2 = i + j + t/2;
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;
}
}
// for garner
static constexpr int MOD0 = 754974721;
static constexpr int MOD1 = 167772161;
static constexpr int MOD2 = 469762049;
using mint0 = Fp<MOD0>;
using mint1 = Fp<MOD1>;
using mint2 = Fp<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> vector<T> naive_mul
(const vector<T>& A, const vector<T>& B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
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> vector<mint> mul
(const vector<mint>& A, const vector<mint>& B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
if (min(N, M) < 30) return naive_mul(A, B);
int MOD = A[0].getmod();
int size_fft = get_fft_size(N, M);
if (MOD == 998244353) {
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];
trans(a), trans(b);
vector<mint> res(size_fft);
for (int i = 0; i < size_fft; ++i) res[i] = a[i] * b[i];
trans(res, true);
res.resize(N + M - 1);
return res;
}
vector<mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
vector<mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
vector<mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
for (int i = 0; i < N; ++i)
a0[i] = A[i].val, a1[i] = A[i].val, a2[i] = A[i].val;
for (int i = 0; i < M; ++i)
b0[i] = B[i].val, b1[i] = B[i].val, b2[i] = B[i].val;
trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), 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];
}
trans(c0, true), trans(c1, true), trans(c2, true);
static const mint mod0 = MOD0, mod01 = mod0 * MOD1;
vector<mint> res(N + M - 1);
for (int i = 0; i < N + M - 1; ++i) {
int y0 = c0[i].val;
int y1 = (imod0 * (c1[i] - y0)).val;
int y2 = (imod01 * (c2[i] - y0) - imod1 * y1).val;
res[i] = mod01 * y2 + mod0 * y1 + y0;
}
return res;
}
// long long
vector<long long> mul_ll
(const vector<long long>& A, const vector<long long>& B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
if (min(N, M) < 30) return naive_mul(A, B);
int size_fft = get_fft_size(N, M);
vector<mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
vector<mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
vector<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];
trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), 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];
}
trans(c0, true), trans(c1, true), trans(c2, true);
static const long long mod0 = MOD0, mod01 = mod0 * MOD1;
vector<long long> res(N + M - 1);
for (int i = 0; i < N + M - 1; ++i) {
int y0 = c0[i].val;
int y1 = (imod0 * (c1[i] - y0)).val;
int y2 = (imod01 * (c2[i] - y0) - imod1 * y1).val;
res[i] = mod01 * y2 + mod0 * y1 + y0;
}
return res;
}
};
// Binomial Coefficient
template<class T> struct BiCoef {
vector<T> fact_, inv_, finv_;
constexpr BiCoef() {}
constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) {
init(n);
}
constexpr void init(int n) noexcept {
fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
int MOD = fact_[0].getmod();
for(int i = 2; i < n; i++){
fact_[i] = fact_[i-1] * i;
inv_[i] = -inv_[MOD%i] * (MOD/i);
finv_[i] = finv_[i-1] * inv_[i];
}
}
constexpr T com(int n, int k) const noexcept {
if (n < k || n < 0 || k < 0) return 0;
return fact_[n] * finv_[k] * finv_[n-k];
}
constexpr T fact(int n) const noexcept {
if (n < 0) return 0;
return fact_[n];
}
constexpr T inv(int n) const noexcept {
if (n < 0) return 0;
return inv_[n];
}
constexpr T finv(int n) const noexcept {
if (n < 0) return 0;
return finv_[n];
}
};
// Formal Power Series
template <typename mint> struct FPS : vector<mint> {
using vector<mint>::vector;
// constructor
FPS(const vector<mint>& r) : vector<mint>(r) {}
// core operator
inline FPS pre(int siz) const {
return FPS(begin(*this), begin(*this) + min((int)this->size(), siz));
}
inline FPS rev() const {
FPS res = *this;
reverse(begin(res), end(res));
return res;
}
inline FPS& normalize() {
while (!this->empty() && this->back() == 0) this->pop_back();
return *this;
}
// basic operator
inline FPS operator - () const noexcept {
FPS res = (*this);
for (int i = 0; i < (int)res.size(); ++i) res[i] = -res[i];
return res;
}
inline FPS operator + (const mint& v) const { return FPS(*this) += v; }
inline FPS operator + (const FPS& r) const { return FPS(*this) += r; }
inline FPS operator - (const mint& v) const { return FPS(*this) -= v; }
inline FPS operator - (const FPS& r) const { return FPS(*this) -= r; }
inline FPS operator * (const mint& v) const { return FPS(*this) *= v; }
inline FPS operator * (const FPS& r) const { return FPS(*this) *= r; }
inline FPS operator / (const mint& v) const { return FPS(*this) /= v; }
inline FPS operator << (int x) const { return FPS(*this) <<= x; }
inline FPS operator >> (int x) const { return FPS(*this) >>= x; }
inline FPS& operator += (const mint& v) {
if (this->empty()) this->resize(1);
(*this)[0] += v;
return *this;
}
inline FPS& operator += (const FPS& r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); ++i) (*this)[i] += r[i];
return this->normalize();
}
inline FPS& operator -= (const mint& v) {
if (this->empty()) this->resize(1);
(*this)[0] -= v;
return *this;
}
inline FPS& operator -= (const FPS& r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); ++i) (*this)[i] -= r[i];
return this->normalize();
}
inline FPS& operator *= (const mint& v) {
for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= v;
return *this;
}
inline FPS& operator *= (const FPS& r) {
return *this = NTT::mul((*this), r);
}
inline FPS& operator /= (const mint& v) {
assert(v != 0);
mint iv = modinv(v);
for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= iv;
return *this;
}
inline FPS& operator <<= (int x) {
FPS res(x, 0);
res.insert(res.end(), begin(*this), end(*this));
return *this = res;
}
inline FPS& operator >>= (int x) {
FPS res;
res.insert(res.end(), begin(*this) + x, end(*this));
return *this = res;
}
inline mint eval(const mint& v){
mint res = 0;
for (int i = (int)this->size()-1; i >= 0; --i) {
res *= v;
res += (*this)[i];
}
return res;
}
inline friend FPS gcd(const FPS& f, const FPS& g) {
if (g.empty()) return f;
return gcd(g, f % g);
}
// advanced operation
// df/dx
inline friend FPS diff(const FPS& f) {
int n = (int)f.size();
FPS res(n-1);
for (int i = 1; i < n; ++i) res[i-1] = f[i] * i;
return res;
}
// \int f dx
inline friend FPS integral(const FPS& f) {
int n = (int)f.size();
FPS res(n+1, 0);
for (int i = 0; i < n; ++i) res[i+1] = f[i] / (i+1);
return res;
}
// inv(f), f[0] must not be 0
inline friend FPS inv(const FPS& f, int deg) {
assert(f[0] != 0);
if (deg < 0) deg = (int)f.size();
FPS res({mint(1) / f[0]});
for (int i = 1; i < deg; i <<= 1) {
res = (res + res - res * res * f.pre(i << 1)).pre(i << 1);
}
res.resize(deg);
return res;
}
inline friend FPS inv(const FPS& f) {
return inv(f, f.size());
}
// division, r must be normalized (r.back() must not be 0)
inline FPS& operator /= (const FPS& r) {
assert(!r.empty());
assert(r.back() != 0);
this->normalize();
if (this->size() < r.size()) {
this->clear();
return *this;
}
int need = (int)this->size() - (int)r.size() + 1;
*this = ((*this).rev().pre(need) * inv(r.rev(), need)).pre(need).rev();
return *this;
}
inline FPS& operator %= (const FPS &r) {
assert(!r.empty());
assert(r.back() != 0);
this->normalize();
FPS q = (*this) / r;
return *this -= q * r;
}
inline FPS operator / (const FPS& r) const { return FPS(*this) /= r; }
inline FPS operator % (const FPS& r) const { return FPS(*this) %= r; }
// log(f) = \int f'/f dx, f[0] must be 1
inline friend FPS log(const FPS& f, int deg) {
assert(f[0] == 1);
FPS res = integral(diff(f) * inv(f, deg));
res.resize(deg);
return res;
}
inline friend FPS log(const FPS& f) {
return log(f, f.size());
}
// exp(f), f[0] must be 0
inline friend FPS exp(const FPS& f, int deg) {
assert(f[0] == 0);
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = res * (f.pre(i<<1) - log(res, i<<1) + 1).pre(i<<1);
}
res.resize(deg);
return res;
}
inline friend FPS exp(const FPS& f) {
return exp(f, f.size());
}
// pow(f) = exp(e * log f)
inline friend FPS pow(const FPS& f, long long e, int deg) {
long long i = 0;
while (i < (int)f.size() && f[i] == 0) ++i;
if (i == (int)f.size()) return FPS(deg, 0);
if (i * e >= deg) return FPS(deg, 0);
mint k = f[i];
FPS res = exp(log((f >> i) / k, deg) * e, deg) * modpow(k, e) << (e * i);
res.resize(deg);
return res;
}
inline friend FPS pow(const FPS& f, long long e) {
return pow(f, e, f.size());
}
// sqrt(f), f[0] must be 1
inline friend FPS sqrt_base(const FPS& f, int deg) {
assert(f[0] == 1);
mint inv2 = mint(1) / 2;
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = (res + f.pre(i << 1) * inv(res, i << 1)).pre(i << 1);
for (mint& x : res) x *= inv2;
}
res.resize(deg);
return res;
}
inline friend FPS sqrt_base(const FPS& f) {
return sqrt_base(f, f.size());
}
};
const int MOD = 1000000007;
using mint = Fp<MOD>;
typedef long long ll;
mint Bostan_Mori(vector<mint> a,vector<mint> c,long long n){
// mulだけ指定
int d = c.size();
for(int i = 0; i < d; i ++) c[i] *= mint(-1);
c.insert(c.begin(),1);
a.insert(a.begin(),0);
a = NTT::mul(a, c);
while(a.size()>1+d)a.pop_back();
while(n!=0){
auto cinv = c;
for(int i=1;i<cinv.size();i+=2)cinv[i] *= -1;
a = NTT::mul(a,cinv);
c = NTT::mul(c,cinv);
{
vector<mint> na;
for(int i=(n&1LL);i<a.size();i+=2)na.push_back(a[i]);
swap(a,na);
}
{
vector<mint> nc;
for(int i=0;i<c.size();i+=2)nc.push_back(c[i]);
swap(c,nc);
}
n>>=1;
}
return a[0] / c[0];
}
vector<mint> get(ll n, vector<ll> v, bool f) {
ll M = (f ? 12 : 13);
M *= n;
vector dp(n + 1, vector<mint> (M + 1, mint(0)));
dp[0][0] = mint(1);
for(ll e : v) {
vector nx = dp;
for(ll i = 0; i <= n; i ++) {
for(ll j = 1; i + j <= n; j ++) {
for(ll k = 0; k <= M; k ++) {
if(k + j * e > M) break;
nx[i + j][k + j * e] += dp[i][k];
}
}
}
swap(nx, dp);
}
return dp.back();
}
int main() {
ll n, p, q;
cin >> n >> p >> q;
vector<ll> a1 = {2, 3, 5, 7, 11, 13};
vector<ll> b1 = {4, 6, 8, 9, 10, 12};
FPS<mint> a(get(p, a1, 0));
FPS<mint> b(get(q, b1, 1));
auto c = a * b;
// ここまで前処理
auto dd = c;
c.erase(c.begin());
mint ans = mint(0);
vector<mint> aa(p * 13 + q * 12, mint(0));
aa.back() = 1;
ll siz = p * 13 + q * 12;
for(ll i = 1; i <= siz; i ++) {
ll m = n - i;
if(m < 0) break;
mint sum = mint(0);
for(int j = i; j <= siz; j ++) {
sum += dd[j];
}
ans += sum * Bostan_Mori(aa, c, siz + m);
}
cout << ans.val << endl;
return 0;
}