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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#809320 | #6137. Sub-cycle Graph | Nelofus | AC ✓ | 87ms | 8336kb | C++20 | 2.3kb | 2024-12-11 14:14:11 | 2024-12-11 14:14:19 |
Judging History
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
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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