#include <bits/stdc++.h>
using namespace std;
inline long long read() {
  long long x = 0;
  long long f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - 48;
    ch = getchar();
  }
  return x * f;
}
const long long maxn = 2000010;
const long long mod = 1e9 + 7;
long long pow_mod(long long a, long long p, long long n) {
  long long res = 1;
  while (p) {
    if (p & 1) res = 1LL * res * a % n;
    a = 1LL * a * a % n;
    p >>= 1;
  }
  return res;
}
long long inv(long long x) { return pow_mod(x % mod, mod - 2, mod); }
long long n, k, y, pre[maxn], suf[maxn], fac[maxn];
long long ans = 0;
int main() {
  n = read();
  k = read();
  fac[0] = pre[0] = suf[k + 3] = 1;
  for (int i = 1; i <= k + 2; ++i) fac[i] = fac[i - 1] * i % mod;
  for (int i = 1; i <= k + 2; ++i) pre[i] = pre[i - 1] * (n - i) % mod;
  for (int i = k + 2; i >= 1; --i) suf[i] = suf[i + 1] * (n - i) % mod;
  for (int i = 1; i <= k + 2; ++i) {
    y = (y + pow_mod(i, k, mod)) % mod;
    long long up = 1LL * pre[i - 1] * suf[i + 1] % mod;
    long long down =
        ((k - i) & 1 ? -1LL : 1LL) * fac[i - 1] * fac[k + 2 - i] % mod;
    ans = (ans + 1LL * y * up % mod * inv(down) % mod) % mod;
  }
  printf("%lld\n", (ans + mod) % mod);
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

There are well-known formulas: <image>, <image>, <image>. Also mathematicians found similar formulas for higher degrees.

Find the value of the sum <image> modulo 109 + 7 (so you should find the remainder after dividing the answer by the value 109 + 7).

Input

The only line contains two integers n, k (1 ≤ n ≤ 109, 0 ≤ k ≤ 106).

Output

Print the only integer a — the remainder after dividing the value of the sum by the value 109 + 7.

Examples

Input

4 1


Output

10


Input

4 2


Output

30


Input

4 3


Output

100


Input

4 0


Output

4

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
inline long long read() {
  long long x = 0;
  long long f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - 48;
    ch = getchar();
  }
  return x * f;
}
const long long maxn = 2000010;
const long long mod = 1e9 + 7;
long long pow_mod(long long a, long long p, long long n) {
  long long res = 1;
  while (p) {
    if (p & 1) res = 1LL * res * a % n;
    a = 1LL * a * a % n;
    p >>= 1;
  }
  return res;
}
long long inv(long long x) { return pow_mod(x % mod, mod - 2, mod); }
long long n, k, y, pre[maxn], suf[maxn], fac[maxn];
long long ans = 0;
int main() {
  n = read();
  k = read();
  fac[0] = pre[0] = suf[k + 3] = 1;
  for (int i = 1; i <= k + 2; ++i) fac[i] = fac[i - 1] * i % mod;
  for (int i = 1; i <= k + 2; ++i) pre[i] = pre[i - 1] * (n - i) % mod;
  for (int i = k + 2; i >= 1; --i) suf[i] = suf[i + 1] * (n - i) % mod;
  for (int i = 1; i <= k + 2; ++i) {
    y = (y + pow_mod(i, k, mod)) % mod;
    long long up = 1LL * pre[i - 1] * suf[i + 1] % mod;
    long long down =
        ((k - i) & 1 ? -1LL : 1LL) * fac[i - 1] * fac[k + 2 - i] % mod;
    ans = (ans + 1LL * y * up % mod * inv(down) % mod) % mod;
  }
  printf("%lld\n", (ans + mod) % mod);
  return 0;
}

```