#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
#define st first
#define nd second
#define pb push_back
#define rep(i,a,b) for(ll i=a;i<=b;i++)
#define all(a) a.begin(),a.end()
const int mxN = 3e3+7;
const int MOD = 1e9+7;
ll mno[mxN];
ll sil[mxN];
ll pot(ll pod,ll wyk){
ll res = 1;
while(wyk){
if(wyk%2 == 1) res *= pod;
pod *= pod;
wyk /= 2;
pod %= MOD;
res %= MOD;
}
return res;
}
ll npok(ll n,ll k){
if(k == 0) return 1;
ll res = sil[n];
res = (res*pot(sil[k],MOD-2))%MOD;
res = (res*pot(sil[n-k],MOD-2))%MOD;
return res;
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0);
ll n,k; cin >> n >> k;
mno[1] = k;
rep(i,2,n) mno[i] = (mno[i-1]*(k-i+1))%MOD;
sil[0] = 1;
rep(i,1,n) sil[i] = (sil[i-1]*i)%MOD;
ll res = 0;
ll i = 1;
while(2*i <= n && i <= k){
ll ress = mno[i];
ress = (ress*npok(n-i-1,i-1))%MOD;
ress = (ress*pot(k,n-2*i))%MOD;
res = (res+ress)%MOD;
i++;
}
cout << res << "\n";
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | #include <bits/stdc++.h> using namespace std; typedef long long ll; typedef long double ld; #define st first #define nd second #define pb push_back #define rep(i,a,b) for(ll i=a;i<=b;i++) #define all(a) a.begin(),a.end() const int mxN = 3e3+7; const int MOD = 1e9+7; ll mno[mxN]; ll sil[mxN]; ll pot(ll pod,ll wyk){ ll res = 1; while(wyk){ if(wyk%2 == 1) res *= pod; pod *= pod; wyk /= 2; pod %= MOD; res %= MOD; } return res; } ll npok(ll n,ll k){ if(k == 0) return 1; ll res = sil[n]; res = (res*pot(sil[k],MOD-2))%MOD; res = (res*pot(sil[n-k],MOD-2))%MOD; return res; } int main(){ ios_base::sync_with_stdio(0); cin.tie(0); ll n,k; cin >> n >> k; mno[1] = k; rep(i,2,n) mno[i] = (mno[i-1]*(k-i+1))%MOD; sil[0] = 1; rep(i,1,n) sil[i] = (sil[i-1]*i)%MOD; ll res = 0; ll i = 1; while(2*i <= n && i <= k){ ll ress = mno[i]; ress = (ress*npok(n-i-1,i-1))%MOD; ress = (ress*pot(k,n-2*i))%MOD; res = (res+ress)%MOD; i++; } cout << res << "\n"; } |
English