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25974.cpp
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25974.cpp
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#include <iostream>
#include <vector>
#define MOD 1000000007
using namespace std;
vector<vector<long long>> precompute(int p) {
vector<vector<long long>> ret(p+1, vector<long long>(p+1, 0));
for (int i=0; i<=p; i++) {
ret[i][0] = ret[i][i] = 1;
for (int j=1; j<=i-1; j++) {
ret[i][j] = (ret[i-1][j] + ret[i-1][j-1]) % MOD;
}
}
return ret;
}
long long power(long long base, long long exp) {
long long ret = 1;
while (exp) {
if (exp & 1) ret = ret * base % MOD;
base = base * base % MOD;
exp >>= 1;
}
return ret;
}
void solve(const vector<vector<long long>> &c) {
int n, p; cin >> n >> p;
vector<long long> ans(p+1, 0); ans[0] = n;
for (int i=1; i<=p; i++) {
ans[i] = power(n+1, i+1) - 1;
for (int j=0; j<=i-1; j++) {
ans[i] = (ans[i] - c[i+1][j] * ans[j] % MOD + MOD) % MOD;
}
ans[i] = ans[i] * power(c[i+1][i], MOD-2) % MOD;
}
cout << ans[p];
}
int main(void) {
ios::sync_with_stdio(false);
cin.tie(nullptr);
vector<vector<long long>> c = precompute(1001);
solve(c);
return 0;
}