結果

問題 No.2120 場合の数の下８桁
コンテスト
ユーザー kwm_t
提出日時 2022-11-04 22:29:27
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 10 ms / 2,000 ms
コード長 8,228 bytes
コンパイル時間 5,621 ms
コンパイル使用メモリ 125,268 KB
最終ジャッジ日時 2025-02-08 18:04:08
ジャッジサーバーID
（参考情報） 		judge5 / judge1
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ファイルパターン 結果
other AC * 20
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ソースコード

diff # 

/**
 *  date : 2021-04-27 12:43:05
 */

#define NDEBUG

#include <cassert>

#include <tuple>

#include <utility>

#include <vector>
#include <string>

 //

using namespace std;

constexpr pair<long long, long long> inv_gcd(long long a, long long b) {
	a = a % b;
	if (a < 0) a += b;
	if (a == 0) return { b, 0 };
	long long s = b, t = a;
	long long m0 = 0, m1 = 1;
	while (t) {
		long long u = s / t;
		s -= t * u;
		m0 -= m1 * u;
		auto tmp = s;
		s = t;
		t = tmp;
		tmp = m0;
		m0 = m1;
		m1 = tmp;
	}
	if (m0 < 0) m0 += b / s;
	return { s, m0 };
}

vector<long long> pre_im(vector<long long> m) {
	vector<long long> ims;
	long long m0 = 1;
	int n = m.size();
	for (int i = 0; i < n; i++) {
		long long m1 = m[i];
		if (m0 < m1) swap(m0, m1);
		long long _, im;
		tie(_, im) = inv_gcd(m0, m1);
		ims.push_back(im);
		m0 *= m1;
	}
	return ims;
}

pair<long long, long long> crt(const vector<long long>& r,
	const vector<long long>& m,
	const vector<long long>& ims) {
	assert(r.size() == m.size());
	int n = int(r.size());
	long long r0 = 0, m0 = 1;
	for (int i = 0; i < n; i++) {
		long long r1 = r[i], m1 = m[i], im = ims[i];
		if (m0 < m1) swap(r0, r1), swap(m0, m1);
		long long x = (r1 - r0) * im % m1;
		r0 += x * m0;
		m0 *= m1;
		if (r0 < 0) r0 += m0;
	}
	return { r0, m0 };
}

using namespace std;

#define PRIME_POWER_BINOMIAL_M_MAX ((1LL << 30) - 1)
#define PRIME_POWER_BINOMIAL_N_MAX 20000000

struct prime_power_binomial {
	int p, q, M;
	vector<int> fac, ifac, inv;
	int delta;

	using i64 = long long;
	using u64 = unsigned long long;
	u64 iM, ip;

	prime_power_binomial(int _p, int _q) : p(_p), q(_q) {
		assert(p <= PRIME_POWER_BINOMIAL_M_MAX);
		assert(_q > 0);
		long long m = 1;
		while (_q--) {
			m *= p;
			assert(m <= PRIME_POWER_BINOMIAL_M_MAX);
		}
		M = m;
		iM = u64(-1) / M + 1;
		ip = u64(-1) / p + 1;

		enumerate();
		delta = (p == 2 && q >= 3) ? 1 : M - 1;
	}

	inline i64 modulo_M(u64 n) {
		u64 x = u64((__uint128_t(n) * iM) >> 64);
		i64 r = i64(n - x * M);
		if (r < 0) r += M;
		return r;
	}

	int modpow(int a, long long e) {
		int r = 1;
		while (e) {
			if (e & 1) r = modulo_M(1LL * r * a);
			a = modulo_M(1LL * a * a);
			e >>= 1;
		}
		return r;
	}

	inline i64 divide_p(u64 n) {
		u64 x = u64((__uint128_t(n) * ip) >> 64);
		i64 r = i64(n - x * p);
		if (r < 0) x--;
		return i64(x);
	}

	inline pair<i64, int> quorem_p(u64 n) {
		u64 x = u64((__uint128_t(n) * ip) >> 64);
		i64 r = i64(n - x * p);
		if (r < 0) r += M, x--;
		return make_pair(i64(x), r);
	}

	void enumerate() {
		int MX = min<int>(M, PRIME_POWER_BINOMIAL_N_MAX + 10);
		fac.resize(MX);
		ifac.resize(MX);
		inv.resize(MX);
		fac[0] = ifac[0] = inv[0] = 1;
		fac[1] = ifac[1] = inv[1] = 1;
		for (int i = 2; i < MX; i++) {
			if (i % p == 0) {
				fac[i] = fac[i - 1];
				fac[i + 1] = modulo_M(1LL * fac[i - 1] * (i + 1));
				i++;
			}
			else {
				fac[i] = modulo_M(1LL * fac[i - 1] * i);
			}
		}
		ifac[MX - 1] = modpow(fac[MX - 1], M / p * (p - 1) - 1);
		for (int i = MX - 2; i > 1; --i) {
			if (i % p == 0) {
				ifac[i] = modulo_M(1LL * ifac[i + 1] * (i + 1));
				ifac[i - 1] = ifac[i];
				i--;
			}
			else {
				ifac[i] = modulo_M(1LL * ifac[i + 1] * (i + 1));
			}
		}
	}

	long long Lucas(long long n, long long m) {
		int res = 1;
		while (n) {
			int n0, m0;
			tie(n, n0) = quorem_p(n);
			tie(m, m0) = quorem_p(m);
			if (n0 < m0) return 0;
			res = modulo_M(1LL * res * fac[n0]);
			res = modulo_M(1LL * res * ifac[m0]);
			res = modulo_M(1LL * res * ifac[n0 - m0]);
		}
		return res;
	}

	long long C(long long n, long long m) {
		if (n < m || n < 0 || m < 0) return 0;
		if (q == 1) return Lucas(n, m);
		long long r = n - m;
		int e0 = 0, eq = 0, i = 0;
		int res = 1;
		while (n) {
			res = modulo_M(1LL * res * fac[modulo_M(n)]);
			res = modulo_M(1LL * res * ifac[modulo_M(m)]);
			res = modulo_M(1LL * res * ifac[modulo_M(r)]);
			n = divide_p(n);
			m = divide_p(m);
			r = divide_p(r);
			int eps = n - m - r;
			e0 += eps;
			if (e0 >= q) return 0;
			if (++i >= q) eq += eps;
		}
		res = modulo_M(1LL * res * modpow(delta, eq));
		res = modulo_M(1LL * res * modpow(p, e0));
		return res;
	}
};

// constraints:
// (M <= 1e7 and max(N) <= 1e18) or (M < 2^30 and max(N) <= 2e7)
struct arbitrary_mod_binomial {
	int mod;
	vector<int> M;
	vector<long long> ims;
	vector<prime_power_binomial> cs;

	arbitrary_mod_binomial(long long md) : mod(md) {
		assert(1 <= md);
		assert(md <= PRIME_POWER_BINOMIAL_M_MAX);
		for (int i = 2; i * i <= md; i++) {
			if (md % i == 0) {
				int j = 0, k = 1;
				while (md % i == 0) md /= i, j++, k *= i;
				M.push_back(k);
				cs.emplace_back(i, j);
				assert(M.back() == cs.back().M);
			}
		}
		if (md != 1) {
			M.push_back(md);
			cs.emplace_back(md, 1);
		}
		assert(M.size() == cs.size());

		vector<long long> ms;
		for (auto& c : cs) ms.push_back(c.M);
		ims = pre_im(ms);
	}

	long long C(long long n, long long m) {
		if (mod == 1) return 0;
		vector<long long> rem, d;
		for (int i = 0; i < (int)cs.size(); i++) {
			rem.push_back(cs[i].C(n, m));
			d.push_back(M[i]);
		}
		return crt(rem, d, ims).first;
	}
};

#undef PRIME_POWER_BINOMIAL_M_MAX
#undef PRIME_POWER_BINOMIAL_N_MAX


#include <cstring>
#include <type_traits>

using namespace std;

namespace fastio {
	static constexpr int SZ = 1 << 17;
	char ibuf[SZ], obuf[SZ];
	int pil = 0, pir = 0, por = 0;

	struct Pre {
		char num[40000];
		constexpr Pre() : num() {
			for (int i = 0; i < 10000; i++) {
				int n = i;
				for (int j = 3; j >= 0; j--) {
					num[i * 4 + j] = n % 10 + '0';
					n /= 10;
				}
			}
		}
	} constexpr pre;

	inline void load() {
		memcpy(ibuf, ibuf + pil, pir - pil);
		pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
		pil = 0;
	}
	inline void flush() {
		fwrite(obuf, 1, por, stdout);
		por = 0;
	}

	inline void skip_space() {
		if (pil + 32 > pir) load();
		while (ibuf[pil] <= ' ') pil++;
	}

	inline void rd(char& c) {
		if (pil + 32 > pir) load();
		c = ibuf[pil++];
	}
	template <typename T>
	inline void rd(T& x) {
		if (pil + 32 > pir) load();
		char c;
		do c = ibuf[pil++];
		while (c < '-');
		[[maybe_unused]] bool minus = false;
		if constexpr (is_signed<T>::value == true) {
			if (c == '-') minus = true, c = ibuf[pil++];
		}
		x = 0;
		while (c >= '0') {
			x = x * 10 + (c & 15);
			c = ibuf[pil++];
		}
		if constexpr (is_signed<T>::value == true) {
			if (minus) x = -x;
		}
	}
	inline void rd() {}
	template <typename Head, typename... Tail>
	inline void rd(Head& head, Tail&... tail) {
		rd(head);
		rd(tail...);
	}

	inline void wt(char c) {
		if (por > SZ - 32) flush();
		obuf[por++] = c;
	}
	inline void wt(bool b) {
		if (por > SZ - 32) flush();
		obuf[por++] = b ? '1' : '0';
	}
	template <typename T>
	inline void wt(T x) {
		if (por > SZ - 32) flush();
		if (!x) {
			obuf[por++] = '0';
			return;
		}
		if constexpr (is_signed<T>::value == true) {
			if (x < 0) obuf[por++] = '-', x = -x;
		}
		int i = 12;
		char buf[16];
		while (x >= 10000) {
			memcpy(buf + i, pre.num + (x % 10000) * 4, 4);
			x /= 10000;
			i -= 4;
		}
		if (x < 100) {
			if (x < 10) {
				obuf[por] = '0' + x;
				++por;
			}
			else {
				uint32_t q = (uint32_t(x) * 205) >> 11;
				uint32_t r = uint32_t(x) - q * 10;
				obuf[por] = '0' + q;
				obuf[por + 1] = '0' + r;
				por += 2;
			}
		}
		else {
			if (x < 1000) {
				memcpy(obuf + por, pre.num + (x << 2) + 1, 3);
				por += 3;
			}
			else {
				memcpy(obuf + por, pre.num + (x << 2), 4);
				por += 4;
			}
		}
		memcpy(obuf + por, buf + i + 4, 12 - i);
		por += 12 - i;
	}

	inline void wt() {}
	template <typename Head, typename... Tail>
	inline void wt(Head&& head, Tail&&... tail) {
		wt(head);
		wt(forward<Tail>(tail)...);
	}
	template <typename... Args>
	inline void wtn(Args&&... x) {
		wt(forward<Args>(x)...);
		wt('\n');
	}

	struct Dummy {
		Dummy() { atexit(flush); }
	} dummy;

}  // namespace fastio
using fastio::rd;
using fastio::skip_space;
using fastio::wt;
using fastio::wtn;

#include <iostream>
int main() {
	unsigned int M, N;
	rd(M, N);
	arbitrary_mod_binomial C(100000000);
	auto val = C.C(M, N);
	string str = to_string(val);
	string ans;
	for (int i = 0; i < 8 - str.size(); ++i)ans += '0';
	ans += str;
	std::cout << ans << endl;
}
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