#include <bits/stdc++.h>
const int mod = 1000000007;
using namespace std;
int Power(int x, int y) {
  int ret = 1;
  while (y) {
    if (y & 1) ret = 1ll * ret * x % mod;
    x = 1ll * x * x % mod, y >>= 1;
  }
  return ret;
}
int n, k, s, t, jc[200005] = {1}, ny[200005] = {1};
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1, x; i <= n; i++) scanf("%d", &x), s = (s + x) % mod;
  if (n == 1) return cout << s, 0;
  for (int i = 1; i <= n; i++) jc[i] = 1ll * jc[i - 1] * i % mod;
  ny[n] = Power(jc[n], mod - 2), s = s;
  for (int i = n - 1; i >= 1; i--) ny[i] = 1ll * (i + 1) * ny[i + 1] % mod;
  for (int i = 0, f = 1; i < k; i++, f = mod - f) {
    t = (t +
         1ll * f * Power(k - i, n - 1) % mod * ny[i] % mod * ny[k - i - 1]) %
        mod;
    t = (t + 1ll * f * Power(k - i, n - 2) % mod * (n - 1) % mod * ny[i] % mod *
                 ny[k - i - 1]) %
        mod;
  }
  cout << 1ll * s * t % mod;
  return 0;
}

### Prompt

Your task is to create a cpp solution to the following problem:

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 = 1000000007;
using namespace std;
int Power(int x, int y) {
  int ret = 1;
  while (y) {
    if (y & 1) ret = 1ll * ret * x % mod;
    x = 1ll * x * x % mod, y >>= 1;
  }
  return ret;
}
int n, k, s, t, jc[200005] = {1}, ny[200005] = {1};
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1, x; i <= n; i++) scanf("%d", &x), s = (s + x) % mod;
  if (n == 1) return cout << s, 0;
  for (int i = 1; i <= n; i++) jc[i] = 1ll * jc[i - 1] * i % mod;
  ny[n] = Power(jc[n], mod - 2), s = s;
  for (int i = n - 1; i >= 1; i--) ny[i] = 1ll * (i + 1) * ny[i + 1] % mod;
  for (int i = 0, f = 1; i < k; i++, f = mod - f) {
    t = (t +
         1ll * f * Power(k - i, n - 1) % mod * ny[i] % mod * ny[k - i - 1]) %
        mod;
    t = (t + 1ll * f * Power(k - i, n - 2) % mod * (n - 1) % mod * ny[i] % mod *
                 ny[k - i - 1]) %
        mod;
  }
  cout << 1ll * s * t % mod;
  return 0;
}

```