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ID题目提交者结果用时内存语言文件大小提交时间测评时间
#94970#6137. Sub-cycle Graphysghwzp#AC ✓121ms4512kbC++201.3kb2023-04-08 15:13:152023-04-08 15:13:19

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-04-08 15:13:19]
  • 评测
  • 测评结果:AC
  • 用时:121ms
  • 内存:4512kb
  • [2023-04-08 15:13:15]
  • 提交

answer

#include <bits/stdc++.h>

using i64 = long long;

constexpr int N = 1E5;
constexpr int P = 1E9 + 7;

int fac[N + 1], invfac[N + 1], inv[N + 1];

int power(int a, int b) {
	int res = 1;
	for (; b; b /= 2, a = 1LL * a * a % P) {
		if (b % 2) {
			res = 1LL * res * a % P;
		}
	}
	return res;
}

int binom(int n, int m) {
	if (n < m || m < 0) {
		return 0;
	}
	return 1LL * fac[n] * invfac[m] % P * invfac[n - m] % P;
}

void solve() {
	int n;
	i64 m;
	std::cin >> n >> m;

	if (n < m) {
		std::cout << 0 << "\n";
		return;
	}

	if (n == m) {
		std::cout << 1LL * fac[n - 1] * (P + 1) / 2 % P << "\n";
		return;
	}

	m = n - m;
	int ans = 0;
	for (int i = 0; i < m; i++) {
		ans = (ans + 1LL * binom(m, i) * binom(n - m + m - i - 1, m - i - 1)) % P;
	}
	if (m == n) {
		ans = (ans + 1) % P;
	}
	ans = 1LL * ans * fac[n] % P * invfac[m] % P * power((P + 1) / 2, m) % P;
	std::cout << ans << "\n";
}

int main() {
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);

	fac[0] = 1;
	for (int i = 1; i <= N; i++) {
		fac[i] = 1LL * fac[i - 1] * i % P;
	}
	invfac[N] = power(fac[N], P - 2);
	for (int i = N; i; i--) {
		invfac[i - 1] = 1LL * invfac[i] * i % P;
		inv[i] = 1LL * invfac[i] * fac[i - 1] % P;
	}

	int T;
	std::cin >> T;

	while (T--) {
		solve();
	}

	return 0;
}

详细

Test #1:

score: 100
Accepted
time: 3ms
memory: 4512kb

input:

3
4 2
4 3
5 3

output:

15
12
90

result:

ok 3 number(s): "15 12 90"

Test #2:

score: 0
Accepted
time: 121ms
memory: 4488kb

input:

17446
3 0
3 1
3 2
3 3
4 0
4 1
4 2
4 3
4 4
5 0
5 1
5 2
5 3
5 4
5 5
6 0
6 1
6 2
6 3
6 4
6 5
6 6
7 0
7 1
7 2
7 3
7 4
7 5
7 6
7 7
8 0
8 1
8 2
8 3
8 4
8 5
8 6
8 7
8 8
9 0
9 1
9 2
9 3
9 4
9 5
9 6
9 7
9 8
9 9
10 0
10 1
10 2
10 3
10 4
10 5
10 6
10 7
10 8
10 9
10 10
11 0
11 1
11 2
11 3
11 4
11 5
11 6
11 7
11...

output:

1
3
3
1
1
6
15
12
3
1
10
45
90
60
12
1
15
105
375
630
360
60
1
21
210
1155
3465
5040
2520
360
1
28
378
2940
13545
35280
45360
20160
2520
1
36
630
6552
42525
170100
393120
453600
181440
20160
1
45
990
13230
114345
643545
2286900
4762800
4989600
1814400
181440
1
55
1485
24750
273735
2047815
10239075
3...

result:

ok 17446 numbers