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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#809320#6137. Sub-cycle GraphNelofusAC ✓87ms8336kbC++202.3kb2024-12-11 14:14:112024-12-11 14:14:19

Judging History

你现在查看的是最新测评结果

  • [2024-12-11 14:14:19]
  • 评测
  • 测评结果:AC
  • 用时:87ms
  • 内存:8336kb
  • [2024-12-11 14:14:11]
  • 提交

answer

// Code by Heratino & Nelofus
#include <bits/stdc++.h>
using i64 = long long;

//{{{
template<typename T>
inline void chkmin(T &a, const T &b) {if (a > b)	a = b;}
template<typename T>
inline void chkmax(T &a, const T &b) {if (a < b)	a = b;}
//}}}

constexpr int N = 3e5 + 10;
constexpr int mod = 1e9 + 7;
inline int fpow(int x, int k) {
	int res = 1;
	for (; k; k >>= 1, x = 1ll * x * x % mod)
		if (k & 1)
			res = 1ll * res * x % mod;
	return res;
}
inline int Add(const int &x, const int &y) {return x + y >= mod ? x + y - mod : x + y;}
inline int Sub(const int &x, const int &y) {return x - y < 0 ? x - y + mod : x - y;}
inline int Mul(const int &x, const int &y) {return 1ll * x * y % mod;}
inline int Div(const int &x, const int &y) {return Mul(x, fpow(y, mod - 2));}
inline void AddTo(int &x, const int &y) {x = Add(x, y);}
inline void SubTo(int &x, const int &y) {x = Sub(x, y);}
inline void MulTo(int &x, const int &y) {x = Mul(x, y);}
inline void DivTo(int &x, const int &y) {x = Div(x, y);}

int fac[N], ifac[N], inv[N], pw[N];
inline int binom(int x, int y) {
	if (x < 0 || y < 0 || y > x)	return 0;
	return Mul(fac[x], Mul(ifac[x - y], ifac[y]));
}

inline void solve() {
	int n, m;
	std::cin >> n >> m;
	if (m > n) {
		std::cout << "0" << '\n';
		return ;
	}
	if (m == n) {
		std::cout << Mul(fac[n - 1], fpow(2, mod - 2)) << '\n';
		return ;
	}
	if (m == 0) {
		std::cout << "1" << '\n';
		return ;
	}
	int k = n - m;
	int ans = 0;
	for (int i = 0, u = n - k; i <= u; i++) {
		if (i > k)	break;
		int j = u - i;
		int t = (i & 1 ? Sub : Add)(0, Mul(binom(k, i), pw[k - i]));
		t = Mul(t, binom(k + j - 1, j));
		AddTo(ans, t);
	}
	ans = Mul(ans, fpow(pw[k], mod - 2));
	std::cout << Mul(ans, Mul(ifac[k], fac[n])) << '\n';
}

int main() {
#ifdef HeratinoNelofus
	freopen("input.txt", "r", stdin);
#endif
	std::ios::sync_with_stdio(false);
	std::cin.tie(nullptr);

	fac[0] = 1, pw[0] = 1;
	for (int i = 1; i < N; i++)
		fac[i] = Mul(fac[i - 1], i), pw[i] = Mul(pw[i - 1], 2);
	ifac[N - 1] = Div(1, fac[N - 1]);
	for (int i = N - 2; i >= 0; i--)
		ifac[i] = Mul(ifac[i + 1], i + 1);
	for (int i = 1; i < N; i++)
		inv[i] = Mul(ifac[i], fac[i - 1]);
	int T;
	std::cin >> T;
	while (T--) {
		solve();
	}
	return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 4ms
memory: 8244kb

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: 87ms
memory: 8336kb

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