#include <bits/stdc++.h>
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
*/
using namespace std;
// using namespace __gnu_pbds;
using namespace chrono;
// mt19937 rng((int) std::chrono::steady_clock::now().time_since_epoch().count());
/*
template <class T> using ordered_set = tree <T, null_type, less <T>, rb_tree_tag, tree_order_statistics_node_update>;
*/
//***************** CONSTANTS *****************
const int64_t MOD = 1'000'000'007;
//***************** GLOBAL VARIABLES *****************
int64_t F[100005], iF[100005];
//***************** AUXILIARY STRUCTS *****************
//***************** MAIN BODY *****************
int64_t power(int64_t n, int64_t x = MOD - 2){
int64_t res = 1;
while(x){
if(x & 1)
res = (res * n) % MOD;
x >>= 1;
n = (n * n) % MOD;
}
return res;
}
inline int64_t nCk(int n, int k){
return F[n] * ((iF[n - k] * iF[k]) % MOD) % MOD;
}
void solve(){
int N, K;
cin >> N >> K;
F[0] = F[1] = 1;
for(int i = 2; i <= N + 1; i++){
F[i] = (F[i-1] * 1LL * i) % MOD;
}
iF[N + 1] = power(F[N + 1]);
for(int i = N; i >= 0; --i){
iF[i] = (iF[i+1] * 1LL * (i + 1)) % MOD;
}
int64_t ans = 0, t = 1;
for(int i = 0; i <= K; i++){
(ans += t*nCk(N + 1, i)*1LL*power(K - i, N)) %= MOD;
ans = (ans + MOD) % MOD;
t = -t;
}
cout << ans << '\n';
}
//***************** *****************
int32_t main(){
ios_base::sync_with_stdio(NULL);
cin.tie(NULL);
#ifdef LOCAL
auto begin = high_resolution_clock::now();
#endif
int tc = 1;
// cin >> tc;
for (int t = 0; t < tc; t++)
solve();
#ifdef LOCAL
auto end = high_resolution_clock::now();
cout << fixed << setprecision(4);
cout << "Execution Time: " << duration_cast<duration<double>>(end - begin).count() << "seconds" << endl;
#endif
return 0;
}
/*
If code gives a WA, check for the following :
1. I/O format
2. Are you clearing all global variables in between tests if multitests are a thing
3. Can you definitively prove the logic
4. If the code gives an inexplicable TLE, and you are sure you have the best possible complexity,
use faster io
*/
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Correct |
0 ms |
204 KB |
Output is correct |
| 3 |
Correct |
1 ms |
204 KB |
Output is correct |
| 4 |
Correct |
1 ms |
204 KB |
Output is correct |
| 5 |
Correct |
0 ms |
204 KB |
Output is correct |
| 6 |
Correct |
0 ms |
204 KB |
Output is correct |
| 7 |
Correct |
0 ms |
204 KB |
Output is correct |
| 8 |
Correct |
0 ms |
204 KB |
Output is correct |
| 9 |
Correct |
0 ms |
204 KB |
Output is correct |
| 10 |
Correct |
0 ms |
204 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Correct |
0 ms |
204 KB |
Output is correct |
| 3 |
Correct |
1 ms |
204 KB |
Output is correct |
| 4 |
Correct |
1 ms |
204 KB |
Output is correct |
| 5 |
Correct |
0 ms |
204 KB |
Output is correct |
| 6 |
Correct |
0 ms |
204 KB |
Output is correct |
| 7 |
Correct |
0 ms |
204 KB |
Output is correct |
| 8 |
Correct |
0 ms |
204 KB |
Output is correct |
| 9 |
Correct |
0 ms |
204 KB |
Output is correct |
| 10 |
Correct |
0 ms |
204 KB |
Output is correct |
| 11 |
Correct |
0 ms |
204 KB |
Output is correct |
| 12 |
Correct |
1 ms |
204 KB |
Output is correct |
| 13 |
Correct |
1 ms |
316 KB |
Output is correct |
| 14 |
Correct |
1 ms |
256 KB |
Output is correct |
| 15 |
Correct |
1 ms |
324 KB |
Output is correct |
| 16 |
Correct |
1 ms |
204 KB |
Output is correct |
| 17 |
Correct |
1 ms |
316 KB |
Output is correct |
| 18 |
Correct |
1 ms |
204 KB |
Output is correct |
| 19 |
Correct |
1 ms |
204 KB |
Output is correct |
| 20 |
Correct |
1 ms |
204 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Correct |
0 ms |
204 KB |
Output is correct |
| 3 |
Correct |
1 ms |
204 KB |
Output is correct |
| 4 |
Correct |
1 ms |
204 KB |
Output is correct |
| 5 |
Correct |
0 ms |
204 KB |
Output is correct |
| 6 |
Correct |
0 ms |
204 KB |
Output is correct |
| 7 |
Correct |
0 ms |
204 KB |
Output is correct |
| 8 |
Correct |
0 ms |
204 KB |
Output is correct |
| 9 |
Correct |
0 ms |
204 KB |
Output is correct |
| 10 |
Correct |
0 ms |
204 KB |
Output is correct |
| 11 |
Correct |
0 ms |
204 KB |
Output is correct |
| 12 |
Correct |
1 ms |
204 KB |
Output is correct |
| 13 |
Correct |
1 ms |
316 KB |
Output is correct |
| 14 |
Correct |
1 ms |
256 KB |
Output is correct |
| 15 |
Correct |
1 ms |
324 KB |
Output is correct |
| 16 |
Correct |
1 ms |
204 KB |
Output is correct |
| 17 |
Correct |
1 ms |
316 KB |
Output is correct |
| 18 |
Correct |
1 ms |
204 KB |
Output is correct |
| 19 |
Correct |
1 ms |
204 KB |
Output is correct |
| 20 |
Correct |
1 ms |
204 KB |
Output is correct |
| 21 |
Correct |
1 ms |
332 KB |
Output is correct |
| 22 |
Correct |
0 ms |
332 KB |
Output is correct |
| 23 |
Correct |
1 ms |
332 KB |
Output is correct |
| 24 |
Correct |
1 ms |
332 KB |
Output is correct |
| 25 |
Correct |
1 ms |
332 KB |
Output is correct |
| 26 |
Correct |
1 ms |
332 KB |
Output is correct |
| 27 |
Correct |
1 ms |
332 KB |
Output is correct |
| 28 |
Correct |
1 ms |
332 KB |
Output is correct |
| 29 |
Correct |
1 ms |
204 KB |
Output is correct |
| 30 |
Correct |
1 ms |
332 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
204 KB |
Output is correct |
| 2 |
Correct |
0 ms |
204 KB |
Output is correct |
| 3 |
Correct |
1 ms |
204 KB |
Output is correct |
| 4 |
Correct |
1 ms |
204 KB |
Output is correct |
| 5 |
Correct |
0 ms |
204 KB |
Output is correct |
| 6 |
Correct |
0 ms |
204 KB |
Output is correct |
| 7 |
Correct |
0 ms |
204 KB |
Output is correct |
| 8 |
Correct |
0 ms |
204 KB |
Output is correct |
| 9 |
Correct |
0 ms |
204 KB |
Output is correct |
| 10 |
Correct |
0 ms |
204 KB |
Output is correct |
| 11 |
Correct |
0 ms |
204 KB |
Output is correct |
| 12 |
Correct |
1 ms |
204 KB |
Output is correct |
| 13 |
Correct |
1 ms |
316 KB |
Output is correct |
| 14 |
Correct |
1 ms |
256 KB |
Output is correct |
| 15 |
Correct |
1 ms |
324 KB |
Output is correct |
| 16 |
Correct |
1 ms |
204 KB |
Output is correct |
| 17 |
Correct |
1 ms |
316 KB |
Output is correct |
| 18 |
Correct |
1 ms |
204 KB |
Output is correct |
| 19 |
Correct |
1 ms |
204 KB |
Output is correct |
| 20 |
Correct |
1 ms |
204 KB |
Output is correct |
| 21 |
Correct |
1 ms |
332 KB |
Output is correct |
| 22 |
Correct |
0 ms |
332 KB |
Output is correct |
| 23 |
Correct |
1 ms |
332 KB |
Output is correct |
| 24 |
Correct |
1 ms |
332 KB |
Output is correct |
| 25 |
Correct |
1 ms |
332 KB |
Output is correct |
| 26 |
Correct |
1 ms |
332 KB |
Output is correct |
| 27 |
Correct |
1 ms |
332 KB |
Output is correct |
| 28 |
Correct |
1 ms |
332 KB |
Output is correct |
| 29 |
Correct |
1 ms |
204 KB |
Output is correct |
| 30 |
Correct |
1 ms |
332 KB |
Output is correct |
| 31 |
Correct |
2 ms |
1868 KB |
Output is correct |
| 32 |
Correct |
3 ms |
1868 KB |
Output is correct |
| 33 |
Correct |
3 ms |
1868 KB |
Output is correct |
| 34 |
Correct |
4 ms |
1868 KB |
Output is correct |
| 35 |
Correct |
10 ms |
1868 KB |
Output is correct |
| 36 |
Correct |
10 ms |
1884 KB |
Output is correct |
| 37 |
Correct |
11 ms |
1880 KB |
Output is correct |
| 38 |
Correct |
2 ms |
460 KB |
Output is correct |
| 39 |
Correct |
5 ms |
1452 KB |
Output is correct |
| 40 |
Correct |
6 ms |
1868 KB |
Output is correct |
