結果

問題 No.215 素数サイコロと合成数サイコロ (3-Hard)
コンテスト
ユーザー btk
提出日時 2015-06-05 07:22:30
言語 C++11（廃止可能性あり）
(gcc 13.3.0)
結果
MLE  
実行時間 -
コード長 9,585 bytes
コンパイル時間 1,255 ms
コンパイル使用メモリ 105,780 KB
実行使用メモリ 128,512 KB
最終ジャッジ日時 2024-07-06 14:09:45
合計ジャッジ時間 11,617 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
other MLE * 1 -- * 1
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ソースコード

diff # 

#include<iostream>
#include<fstream>
#include<vector>
#include<list>
#include<algorithm>
#include<utility>
#include<complex>
#include<functional>
#include<cassert>
using namespace std;
#define reE(i,a,b) for(auto (i)=(a);(i)<=(b);(i)++)
#define rE(i,b) reE(i,0,b)
#define reT(i,a,b) for(auto (i)=(a);(i)<(b);(i)++)
#define rT(i,b) reT(i,0,b)
#define rep(i,a,b) reE(i,a,b);
#define rev(i,a,b) for(auto (i)=(b)-1;(i)>=(a);(i)--)
#define itr(i,b) for(auto (i)=(b).begin();(i)!=(b).end();++(i))
#define LL long long

#define BUFFSIZE (long long)7510

#define MAX_LOGN 60

typedef long long ll;
typedef pair<int, int> Pii;

#define FOR(i,n) for(int i = 0; i < (n); i++)
#define sz(c) ((int)(c).size())
#define ten(x) ((int)1e##x)

template<class T> T extgcd(T a, T b, T& x, T& y) { for (T u = y = 1, v = x = 0; a;) { T q = b / a; swap(x -= q * u, u); swap(y -= q * v, v); swap(b -= q * a, a); } return b; }
template<class T> T mod_inv(T a, T m) { T x, y; extgcd(a, m, x, y); return (m + x % m) % m; }
ll mod_pow(ll a, ll n, ll mod) { ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }

template<int mod, int primitive_root>
class NTT {
public:
	int get_mod() const { return mod; }
	void _ntt(vector<ll>& a, int sign) {
		const int n = sz(a);
		assert((n ^ (n&-n)) == 0); //n = 2^k

		const int g = 3; //g is primitive root of mod
		int h = (int)mod_pow(g, (mod - 1) / n, mod); // h^n = 1
		if (sign == -1) h = (int)mod_inv(h, mod); //h = h^-1 % mod

		//bit reverse
		int i = 0;
		for (int j = 1; j < n - 1; ++j) {
			for (int k = n >> 1; k >(i ^= k); k >>= 1);
			if (j < i) swap(a[i], a[j]);
		}

		for (int m = 1; m < n; m *= 2) {
			const int m2 = 2 * m;
			const ll base = mod_pow(h, n / m2, mod);
			ll w = 1;
			FOR(x, m) {
				for (int s = x; s < n; s += m2) {
					ll u = a[s];
					ll d = a[s + m] * w % mod;
					a[s] = u + d;
					if (a[s] >= mod) a[s] -= mod;
					a[s + m] = u - d;
					if (a[s + m] < 0) a[s + m] += mod;
				}
				w = w * base % mod;
			}
		}

		for (auto& x : a) if (x < 0) x += mod;
	}
	void ntt(vector<ll>& input) {
		_ntt(input, 1);
	}
	void intt(vector<ll>& input) {
		_ntt(input, -1);
		const int n_inv = mod_inv(sz(input), mod);
		for (auto& x : input) x = x * n_inv % mod;
	}

	// 畳み込み演算を行う
	vector<ll> convolution(const vector<ll>& a, const vector<ll>& b){
		int ntt_size = 1;
		while (ntt_size < sz(a) + sz(b)) ntt_size *= 2;

		vector<ll> _a = a, _b = b;
		_a.resize(ntt_size); _b.resize(ntt_size);

		ntt(_a);
		ntt(_b);

		FOR(i, ntt_size){
			(_a[i] *= _b[i]) %= mod;
		}

		intt(_a);
		return _a;
	}
};

ll garner(vector<Pii> mr, int mod){
	mr.emplace_back(mod, 0);

	vector<ll> coffs(sz(mr), 1);
	vector<ll> constants(sz(mr), 0);
	FOR(i, sz(mr) - 1){
		// coffs[i] * v + constants[i] == mr[i].second (mod mr[i].first) を解く
		ll v = (mr[i].second - constants[i]) * mod_inv<ll>(coffs[i], mr[i].first) % mr[i].first;
		if (v < 0) v += mr[i].first;

		for (int j = i + 1; j < sz(mr); j++) {
			(constants[j] += coffs[j] * v) %= mr[j].first;
			(coffs[j] *= mr[i].first) %= mr[j].first;
		}
	}

	return constants[sz(mr) - 1];
}

typedef NTT<167772161, 3> NTT_1;
typedef NTT<469762049, 3> NTT_2;
typedef NTT<1224736769, 3> NTT_3;

//任意のmodで畳み込み演算 O(n log n)
vector<ll> int32mod_convolution(vector<ll> a, vector<ll> b, int mod){
	for (auto& x : a) x %= mod;
	for (auto& x : b) x %= mod;
	NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;
	auto x = ntt1.convolution(a, b);
	auto y = ntt2.convolution(a, b);
	auto z = ntt3.convolution(a, b);

	vector<ll> ret(sz(x));
	vector<Pii> mr(3);
	FOR(i, sz(x)){
		mr[0].first = ntt1.get_mod(), mr[0].second = (int)x[i];
		mr[1].first = ntt2.get_mod(), mr[1].second = (int)y[i];
		mr[2].first = ntt3.get_mod(), mr[2].second = (int)z[i];
		ret[i] = garner(mr, mod);
	}

	return ret;
}

// garnerのアルゴリズムを直書きしたversion，速い
vector<ll> fast_int32mod_convolution(vector<ll> a, vector<ll> b, int mod){
	for (auto& x : a) x %= mod;
	for (auto& x : b) x %= mod;

	NTT_1 ntt1; NTT_2 ntt2; NTT_3 ntt3;
	assert(ntt1.get_mod() < ntt2.get_mod() && ntt2.get_mod() < ntt3.get_mod());
	auto x = ntt1.convolution(a, b);
	auto y = ntt2.convolution(a, b);
	auto z = ntt3.convolution(a, b);

	// garnerのアルゴリズムを極力高速化した
	const ll m1 = ntt1.get_mod(), m2 = ntt2.get_mod(), m3 = ntt3.get_mod();
	const ll m1_inv_m2 = mod_inv<ll>(m1, m2);
	const ll m12_inv_m3 = mod_inv<ll>(m1 * m2, m3);
	const ll m12_mod = m1 * m2 % mod;
	vector<ll> ret(sz(x));
	FOR(i, sz(x)){
		ll v1 = (y[i] - x[i]) *  m1_inv_m2 % m2;
		if (v1 < 0) v1 += m2;
		ll v2 = (z[i] - (x[i] + m1 * v1) % m3) * m12_inv_m3 % m3;
		if (v2 < 0) v2 += m3;
		ll constants3 = (x[i] + m1 * v1 + m12_mod * v2) % mod;
		if (constants3 < 0) constants3 += mod;
		ret[i] = constants3;
	}

	return ret;
}
#define MOD 1000000007
template <class T>
class Mr{
public:
	vector<T> first;
	vector<T> C;
	vector<vector<T>> bin;
	vector<T> t;
	vector<LL> lw, rw;//M+1個の作業用
	vector<LL> lu, ru;//M個の作業用
	ofstream cout;
	T zero, one;
	int M;
	//n(1,,,2M)をn(1,,,M)に修正、O(M^2)
	void form(vector<T> &n){

		vector<T> ttttt = n;
		rev(i, M + 1, 2 * M + 1)
		if (ttttt[i].val){
		reE(j, 1, M)ttttt[i - j] = (ttttt[i - j] + (C[M - j] * n[i]));
		//ttttt[i] = zero;
		}
		
		for (int i = 0; i < M; i++){
			lu[i] = t[i].val;
			ru[i] = n[2 * M - i].val;
		}
		auto b = fast_int32mod_convolution(lu, ru, MOD);
		for (int i = 0; i < M; i++){
			rw[i] = b[i];
			lw[i + 1] = C[M - i - 1].val;
		}
		rw[M] = 0;
		lw[0] = 0;
		auto bb = fast_int32mod_convolution(lw, rw, MOD);
		n[0] = zero;
		for (int i = 1; i <= M; i++){
			n[i] = (n[i].val + bb[2*M - i])%MOD;
			n[M + i] = zero;
		}

		for (int i = 1; i <= M; i++){
			cout << "(" << n[i].val << "," << ttttt[i].val << ")";
		}
		cout << endl;
	}
	//lとrを足し合わせる、O(M^2)
	inline void add(vector<T> &l, vector<T> &r, vector<T> &ans){
		lw[0] = 0;
		rw[0] = 0;
		for (int i = 1; i <= M; i++){
			lw[i] = l[i].val;
			rw[i] = r[i].val;
		}
		auto tmp = fast_int32mod_convolution(lw, rw, MOD);
		reE(i, 1, 2 * M)ans[i].val = tmp[i];

		form(ans);
	}
	//初期化、O(M*MAX_LOGN)
	Mr(const vector<T>& f, const vector<T>& c, int m, T e1, T e0){
		cout.open("a.txt", ios::out);
		M = m;
		first.reserve(M + 1); C.reserve(M);
		lw.resize(M + 1);
		rw.resize(M + 1);
		lu.resize(M);
		ru.resize(M);
		zero = e0, one = e1;
		first.push_back(zero);
		rT(i, M){ first.push_back(f[i]); C.push_back(c[i]); }

		t.resize(M);
		t[0] = one;
		for (int i = 0; i < M; i++)
			for (int j = i+1; j < M; j++){
				t[j] = t[j] + C[M - (j - i)]*t[i];
			}

		bin.resize(MAX_LOGN);
		rT(i, MAX_LOGN)bin[i].resize(2 * M + 1);
		rE(i, 2 * M)bin[0][i] = zero; bin[0][1] = one;
		reT(i, 1, MAX_LOGN){
			add(bin[i - 1], bin[i - 1], bin[i]);
		}
		
	}
	//N項目の計算、戻り値がTの形であることに注意、O(M^2*logN)
	vector<T> calc(LL n){
		n--;
		vector<T> tmp, result = bin[0];
		for (int b = 0; n; b++, n >>= 1)
			if (1 & n){ tmp = result; add(tmp, bin[b], result); }
		//reE(i, 1, M)ans = ans + (result[i] * first[i]);
		return result;
	}
};
//テンプレート、デフォルトコンストラクタのオーバーロードを忘れない

struct X{
	LL val;
	X(LL  v){ val = v; }
	X(){ val = 0; }
	LL operator=(const X &another){ return val = another.val; }
	LL operator*(const X &another)const{ return (val*another.val) % MOD; }
	LL operator+(const X &another)const{ return (val + another.val) % MOD; }
};

LL comb[BUFFSIZE + 1];
LL temp[301][BUFFSIZE + 1][6];
LL dp[2 * BUFFSIZE + 1] = { 1 };
LL sumc[BUFFSIZE + 1] = { 0 };
int sosuu[] = { 2, 3, 5, 7, 11, 13 }, gousei[] = { 4, 6, 8, 9, 10, 12 };
int p, c;


vector<X> C(BUFFSIZE + 1);
int main(void){
	LL N;
	cin >> N >> p >> c;
	//combの計算
	temp[0][0][0] = 1;
	for (int n = 0; n<p; n++)
		for (int j = 0; j < 6; j++)
			for (int i = sosuu[j]; i <= BUFFSIZE; i++)
				for (int k = 0; k <= j; k++)
					temp[n + 1][i][j] = (temp[n + 1][i][j] + temp[n][i - sosuu[j]][k]) % MOD;
	if (p)for (int i = 0; i <= BUFFSIZE; i++){
		temp[0][i][0] = 0;
		for (int j = 0; j < 6; j++)
			temp[0][i][0] = (temp[0][i][0] + temp[p][i][j]) % MOD;
	}
	for (int i = 1; i <= p; i++)
		for (int j = 0; j <= BUFFSIZE; j++)
			for (int k = 0; k<6; k++)
				temp[i][j][k] = 0;
	for (int n = 0; n<c; n++)
		for (int j = 0; j < 6; j++)
			for (int i = gousei[j]; i <= BUFFSIZE; i++)
				for (int k = 0; k <= j; k++)
					temp[n + 1][i][j] = (temp[n + 1][i][j] + temp[n][i - gousei[j]][k]) % MOD;
	for (int i = 0; i <= BUFFSIZE; i++)
		for (int j = 0; j < 6; j++)
			comb[i] = (comb[i] + temp[c][i][j]) % MOD;
	//漸化式の初項部分
	for (LL i = 0; i <= 2 * BUFFSIZE; i++){
		for (LL j = 1; j <= min(i, BUFFSIZE); j++){
			dp[i] = (dp[i] + comb[j] * dp[i - j]) % MOD;
		}
	}
	//漸化式の係数部分
	for (int i = 1; i <= BUFFSIZE; i++){
		C[BUFFSIZE - i] = X(comb[i]);
	}
	for (int i = BUFFSIZE - 1; i >= 0; i--){
		sumc[i] = (sumc[i + 1] + comb[i]) % MOD;
	}
	LL res = 0;
	if (N < BUFFSIZE + 100){
		for (LL i = 0; i < min(N, BUFFSIZE); i++)
			res = (res + dp[i] * sumc[min(N, BUFFSIZE) - i]) % MOD;
	}
	else{
		//	cout << "M" << endl;
		Mr<X> mr(C, C, BUFFSIZE, X(1), X(0));

		auto cc = mr.calc(N + 1 - BUFFSIZE);

		//	cout << "M" << endl;
		for (LL i = 0; i < BUFFSIZE; i++)
			if (sumc[BUFFSIZE - i]){
				LL x = 0;
				for (int j = 0; j < BUFFSIZE; j++)
					x = (x + dp[i + j] * cc[j + 1].val) % MOD;
				res = (res + x*sumc[BUFFSIZE - i]) % MOD;
				//		cout << i << endl;
			}
	}
	cout << res << endl;
	return(0);
}
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