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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#496983 | #6137. Sub-cycle Graph | ucup-team1198# | AC ✓ | 80ms | 6768kb | C++14 | 2.0kb | 2024-07-28 17:41:06 | 2024-07-28 17:41:10 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
int add(int a, int b) {
return a + b >= MOD ? a + b - MOD : a + b;
}
int sub(int a, int b) {
return a >= b ? a - b : a + MOD - b;
}
int mul(int a, int b) {
return (1ll * a * b) % MOD;
}
int pw(int x, int n) {
int res = 1;
while (n) {
if (n % 2 == 0) {
x = mul(x, x);
n /= 2;
} else {
res = mul(res, x);
--n;
}
}
return res;
}
const int MAXF = 2e5 + 100;
int fact[MAXF], invf[MAXF];
const int HALF = (MOD + 1) / 2;
int pw2[MAXF], invpw2[MAXF];
int C(int n, int k) {
if (k < 0 || k > n) return 0;
return mul(fact[n], mul(invf[k], invf[n - k]));
}
void solve_() {
int n;
int64_t m;
cin >> n >> m;
if (m > n) {
cout << "0\n";
return;
}
if (m == n) {
cout << mul(fact[n - 1], HALF) << "\n";
return;
}
int l = n - m;
int ans = 0;
for (int i = 0; i <= m; ++i) {
if (m - i > n - m) continue;
int cur = C(i + l - 1, l - 1);
cur = mul(cur, C(l, m - i));
cur = mul(cur, pw2[n - 2 * m + i]);
if ((m - i) % 2 == 0) {
ans = add(ans, cur);
} else {
ans = sub(ans, cur);
}
}
ans = mul(ans, fact[n]);
ans = mul(ans, invf[l]);
ans = mul(ans, invpw2[n - m]);
cout << ans << "\n";
}
#define MULTITEST
main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
fact[0] = 1;
pw2[0] = invpw2[0] = 1;
for (int i = 1; i < MAXF; ++i) {
fact[i] = mul(fact[i - 1], i);
pw2[i] = mul(pw2[i - 1], 2);
invpw2[i] = mul(invpw2[i - 1], HALF);
}
invf[MAXF - 1] = pw(fact[MAXF - 1], MOD - 2);
for (int i = MAXF - 1; i > 0; --i) {
invf[i - 1] = mul(invf[i], i);
}
int tst = 1;
#ifdef MULTITEST
cin >> tst;
#endif // MULTITEST
while (tst--) {
solve_();
}
return 0;
}
Details
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Test #1:
score: 100
Accepted
time: 4ms
memory: 6768kb
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: 80ms
memory: 6756kb
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