#include <bits/stdc++.h>
const int MOD = 1e9 + 7;
inline int Qpow(int a, int b) {
  int ans = 1;
  for (; b; a = 1LL * a * a % MOD, b >>= 1)
    if (b & 1) ans = 1LL * ans * a % MOD;
  return ans;
}
inline int inv(int x) { return Qpow(x, MOD - 2); }
int n, K;
inline int S(int n, int m) {
  if (n < m) return 0;
  int ans = 0, fac = 1;
  for (int i = 1; i <= m; ++i) fac = 1LL * fac * i % MOD;
  for (int i = 0, pro = 1; i <= m; ++i) {
    ans = (ans + 1LL * Qpow(MOD - 1, m - i) * inv(pro) % MOD * Qpow(i, n) %
                     MOD * inv(fac)) %
          MOD;
    fac = 1LL * fac * inv(m - i) % MOD, pro = 1LL * pro * (i + 1) % MOD;
  }
  return ans;
}
int main() {
  scanf("%d%d", &n, &K);
  int sum = 0;
  for (int i = 1, x; i <= n; ++i) scanf("%d", &x), sum = (sum + x) % MOD;
  int ans = 1LL * sum * (S(n, K) + 1LL * (n - 1) * S(n - 1, K) % MOD) % MOD;
  printf("%d\n", ans);
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

You are given a set of n elements indexed from 1 to n. The weight of i-th element is wi. The weight of some subset of a given set is denoted as <image>. The weight of some partition R of a given set into k subsets is <image> (recall that a partition of a given set is a set of its subsets such that every element of the given set belongs to exactly one subset in partition).

Calculate the sum of weights of all partitions of a given set into exactly k non-empty subsets, and print it modulo 109 + 7. Two partitions are considered different iff there exist two elements x and y such that they belong to the same set in one of the partitions, and to different sets in another partition.

Input

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 2·105) — the number of elements and the number of subsets in each partition, respectively.

The second line contains n integers wi (1 ≤ wi ≤ 109)— weights of elements of the set.

Output

Print one integer — the sum of weights of all partitions of a given set into k non-empty subsets, taken modulo 109 + 7.

Examples

Input

4 2
2 3 2 3


Output

160


Input

5 2
1 2 3 4 5


Output

645

Note

Possible partitions in the first sample:

  1. {{1, 2, 3}, {4}}, W(R) = 3·(w1 + w2 + w3) + 1·w4 = 24; 
  2. {{1, 2, 4}, {3}}, W(R) = 26; 
  3. {{1, 3, 4}, {2}}, W(R) = 24; 
  4. {{1, 2}, {3, 4}}, W(R) = 2·(w1 + w2) + 2·(w3 + w4) = 20; 
  5. {{1, 3}, {2, 4}}, W(R) = 20; 
  6. {{1, 4}, {2, 3}}, W(R) = 20; 
  7. {{1}, {2, 3, 4}}, W(R) = 26; 



Possible partitions in the second sample:

  1. {{1, 2, 3, 4}, {5}}, W(R) = 45; 
  2. {{1, 2, 3, 5}, {4}}, W(R) = 48; 
  3. {{1, 2, 4, 5}, {3}}, W(R) = 51; 
  4. {{1, 3, 4, 5}, {2}}, W(R) = 54; 
  5. {{2, 3, 4, 5}, {1}}, W(R) = 57; 
  6. {{1, 2, 3}, {4, 5}}, W(R) = 36; 
  7. {{1, 2, 4}, {3, 5}}, W(R) = 37; 
  8. {{1, 2, 5}, {3, 4}}, W(R) = 38; 
  9. {{1, 3, 4}, {2, 5}}, W(R) = 38; 
  10. {{1, 3, 5}, {2, 4}}, W(R) = 39; 
  11. {{1, 4, 5}, {2, 3}}, W(R) = 40; 
  12. {{2, 3, 4}, {1, 5}}, W(R) = 39; 
  13. {{2, 3, 5}, {1, 4}}, W(R) = 40; 
  14. {{2, 4, 5}, {1, 3}}, W(R) = 41; 
  15. {{3, 4, 5}, {1, 2}}, W(R) = 42. 

### Response

```cpp
#include <bits/stdc++.h>
const int MOD = 1e9 + 7;
inline int Qpow(int a, int b) {
  int ans = 1;
  for (; b; a = 1LL * a * a % MOD, b >>= 1)
    if (b & 1) ans = 1LL * ans * a % MOD;
  return ans;
}
inline int inv(int x) { return Qpow(x, MOD - 2); }
int n, K;
inline int S(int n, int m) {
  if (n < m) return 0;
  int ans = 0, fac = 1;
  for (int i = 1; i <= m; ++i) fac = 1LL * fac * i % MOD;
  for (int i = 0, pro = 1; i <= m; ++i) {
    ans = (ans + 1LL * Qpow(MOD - 1, m - i) * inv(pro) % MOD * Qpow(i, n) %
                     MOD * inv(fac)) %
          MOD;
    fac = 1LL * fac * inv(m - i) % MOD, pro = 1LL * pro * (i + 1) % MOD;
  }
  return ans;
}
int main() {
  scanf("%d%d", &n, &K);
  int sum = 0;
  for (int i = 1, x; i <= n; ++i) scanf("%d", &x), sum = (sum + x) % MOD;
  int ans = 1LL * sum * (S(n, K) + 1LL * (n - 1) * S(n - 1, K) % MOD) % MOD;
  printf("%d\n", ans);
  return 0;
}

```