#666470 (C++17) No.1489 Repeat Cumulative Sum

提出ソース

結果

問題	No.1489 Repeat Cumulative Sum
ユーザー	tkmst201
提出日時	2021-06-13 22:03:01
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	18 ms / 2,000 ms
コード長	5,264 bytes
コンパイル時間	2,150 ms
コンパイル使用メモリ	205,720 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-06-06 02:18:25
合計ジャッジ時間	3,197 ms
ジャッジサーバーID （参考情報）	judge3 / judge5

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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	2 ms 6,816 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	1 ms 6,940 KB
testcase_03	AC	13 ms 6,940 KB
testcase_04	AC	14 ms 6,940 KB
testcase_05	AC	15 ms 6,944 KB
testcase_06	AC	12 ms 6,940 KB
testcase_07	AC	9 ms 6,940 KB
testcase_08	AC	6 ms 6,940 KB
testcase_09	AC	18 ms 6,944 KB
testcase_10	AC	14 ms 6,940 KB
testcase_11	AC	12 ms 6,944 KB
testcase_12	AC	2 ms 6,944 KB
testcase_13	AC	10 ms 6,940 KB
testcase_14	AC	15 ms 6,944 KB
testcase_15	AC	16 ms 6,944 KB
testcase_16	AC	8 ms 6,944 KB
testcase_17	AC	9 ms 6,944 KB
testcase_18	AC	7 ms 6,940 KB
testcase_19	AC	6 ms 6,940 KB
testcase_20	AC	7 ms 6,940 KB
testcase_21	AC	11 ms 6,944 KB
testcase_22	AC	3 ms 6,940 KB
testcase_23	AC	5 ms 6,944 KB
testcase_24	AC	1 ms 6,940 KB
testcase_25	AC	4 ms 6,940 KB
testcase_26	AC	17 ms 6,940 KB
testcase_27	AC	10 ms 6,940 KB
testcase_28	AC	2 ms 6,944 KB
testcase_29	AC	7 ms 6,944 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) begin(v),end(v)
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
using ll = long long;
using pii = pair<int, int>;
constexpr ll INF = 1ll<<30;
constexpr ll longINF = 1ll<<60;
constexpr ll MOD = 1000000007;
constexpr bool debug = false;
//---------------------------------//

/**
 * @brief https://tkmst201.github.io/Library/Mathematics/ModInt.hpp
 */
template<int M>
struct ModInt {
	static_assert(M > 0);
	
	using value_type = int;
	using calc_type = std::int_fast64_t;
	
private:
	value_type val_;
	
public:
	constexpr ModInt(calc_type val = 0) : val_(val % M + (val >= 0 ? 0 : M)) {}
	constexpr value_type val() const noexcept { return val_; }
	constexpr static decltype(M) mod() noexcept { return M; }
	
	explicit constexpr operator bool() const noexcept { return val_; }
	constexpr bool operator !() const noexcept { return !static_cast<bool>(*this); }
	constexpr ModInt operator +() const noexcept { return *this; }
	constexpr ModInt operator -() const noexcept { return ModInt(val_ == 0 ? 0 : M - val_); }
	constexpr ModInt operator ++(int) noexcept { ModInt res = *this; ++*this; return res; }
	constexpr ModInt operator --(int) noexcept { ModInt res = *this; --*this; return res; }
	constexpr ModInt & operator ++() noexcept { val_ = val_ + 1 == M ? 0 : val_ + 1; return *this; }
	constexpr ModInt & operator --() noexcept { val_ = val_ == 0 ? M - 1 : val_ - 1; return *this; }
	constexpr ModInt & operator +=(const ModInt & rhs) noexcept { val_ += val_ < M - rhs.val_ ? rhs.val_ : rhs.val_ - M; return *this; }
	constexpr ModInt & operator -=(const ModInt & rhs) noexcept { val_ += val_ >= rhs.val_ ? -rhs.val_ : M - rhs.val_; return *this; }
	constexpr ModInt & operator *=(const ModInt & rhs) noexcept { val_ = static_cast<calc_type>(val_) * rhs.val_ % M; return *this; }
	constexpr ModInt & operator /=(const ModInt & rhs) noexcept { return *this *= rhs.inv(); }
	friend constexpr ModInt operator +(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) += rhs; }
	friend constexpr ModInt operator -(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) -= rhs; }
	friend constexpr ModInt operator *(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) *= rhs; }
	friend constexpr ModInt operator /(const ModInt & lhs, const ModInt & rhs) noexcept { return ModInt(lhs) /= rhs; }
	friend constexpr bool operator ==(const ModInt & lhs, const ModInt & rhs) noexcept { return lhs.val_ == rhs.val_; }
	friend constexpr bool operator !=(const ModInt & lhs, const ModInt & rhs) noexcept { return !(lhs == rhs); }
	friend std::ostream & operator <<(std::ostream & os, const ModInt & rhs) { return os << rhs.val_; }
	friend std::istream & operator >>(std::istream & is, ModInt & rhs) { calc_type x; is >> x; rhs = ModInt(x); return is; }
	
	constexpr ModInt pow(calc_type n) const noexcept {
		ModInt res = 1, x = val_;
		if (n < 0) { x = x.inv(); n = -n; }
		while (n) { if (n & 1) res *= x; x *= x; n >>= 1; }
		return res;
	}
	
	constexpr ModInt inv() const noexcept {
		value_type a = val_, a1 = 1, b = M, b1 = 0;
		while (b > 0) {
			const value_type q = a / b;
			value_type tmp = a - q * b; a = b; b = tmp;
			tmp = a1 - q * b1; a1 = b1; b1 = tmp;
		}
		assert(a == 1);
		if (a1 < 0) a1 += M;
		return a1;
	}
};
using mint = ModInt<MOD>;

/**
 * @brief https://tkmst201.github.io/Library/Mathematics/Combination.hpp
 */
template<typename T>
struct Combination {
	using size_type = std::size_t;
	
private:
	std::vector<T> fact_, finv_, inv_;
	static constexpr size_type MAX_LIMIT = 50000000;
	
public:
	explicit Combination(size_type sz = 1) : fact_(1, 1), finv_(1, 1), inv_(1, 1) { build(sz); }
	
	T fact(size_type k) { if (k >= T::mod()) return 0; build(k); return fact_[k]; }
	T finv(size_type k) { assert(k < T::mod()); build(k); return finv_[k]; }
	T inv(size_type k) { assert(k > 0 && k < T::mod()); build(k); return inv_[k]; }
	T operator ()(int n, int r) { return c(n, r); }
	T c(int n, int r) {
		if (r < 0 || n < r) return 0;
		return fact(n) * finv(r) * finv(n - r);
	}
	
private:
	void build(size_type k) {
		if (fact_.size() > k) return;
		assert(k < MAX_LIMIT);
		size_type sz = std::min({MAX_LIMIT, static_cast<size_type>(T::mod()), std::max(fact_.size() * 2, k + 1)});
		size_type presz = fact_.size();
		fact_.resize(sz);
		finv_.resize(sz);
		inv_.resize(sz);
		for (size_type i = presz; i < sz; ++i) fact_[i] = fact_[i - 1] * i;
		finv_[sz - 1] = fact_[sz - 1].inv();
		for (size_type i = sz - 1; i > presz; --i) {
			finv_[i - 1] = finv_[i] * i;
			inv_[i] = fact_[i - 1] * finv_[i];
		}
		inv_[presz] = fact_[presz - 1] * finv_[presz];
	}
};
using Comb = Combination<mint>;
Comb comb;

int main() {
	int N;
	ll M;
	cin >> N >> M;
	mint ans = 0;
	vector<mint> p(N);
	p[0] = 1;
	FOR(i, 1, N) p[i] = p[i - 1] * (M - 1 + i);
	
	FOR(i, 1, N) {
		int a;
		scanf("%d", &a);
		mint pat = p[N - i] * comb.finv(N - i);
		ans += a * pat;
	}
	cout << ans << endl;
}

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