#include <bits/stdc++.h>
using namespace std;
const long long N = 1e5 + 10;
const long long MOD = 1e9 + 7;
long long qpow(long long a, long long b) {
  if (b == 0)
    return 1;
  else if (b % 2 == 1)
    return (a * qpow(a, b - 1)) % MOD;
  else {
    long long ret = qpow(a, b / 2);
    return (ret * ret) % MOD;
  }
}
long long stirling(int n, int k) {
  long long coef = 0;
  long long dwumian = 1;
  for (int j = 0; j <= k; j++) {
    long long pom = 1;
    pom *= dwumian;
    pom %= MOD;
    pom *= qpow(j, n);
    pom %= MOD;
    if ((j + k) % 2) pom *= -1;
    coef += pom;
    coef %= MOD;
    dwumian *= (k - j);
    dwumian %= MOD;
    dwumian *= qpow(j + 1, MOD - 2);
    dwumian %= MOD;
  }
  long long silnia = 1;
  for (int i = 2; i <= k; i++) {
    silnia *= i;
    silnia %= MOD;
  }
  coef *= qpow(silnia, MOD - 2);
  coef %= MOD;
  return coef;
}
int main() {
  int n, k;
  cin >> n >> k;
  long long res = 0;
  long long coef = stirling(n, k) + (n - 1) * stirling(n - 1, k);
  coef %= MOD;
  for (int i = 0; i < n; i++) {
    long long w;
    cin >> w;
    res += w * coef;
    res %= MOD;
  }
  res += MOD;
  res %= MOD;
  cout << res;
}

### Prompt

In cpp, your task is to solve 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>
using namespace std;
const long long N = 1e5 + 10;
const long long MOD = 1e9 + 7;
long long qpow(long long a, long long b) {
  if (b == 0)
    return 1;
  else if (b % 2 == 1)
    return (a * qpow(a, b - 1)) % MOD;
  else {
    long long ret = qpow(a, b / 2);
    return (ret * ret) % MOD;
  }
}
long long stirling(int n, int k) {
  long long coef = 0;
  long long dwumian = 1;
  for (int j = 0; j <= k; j++) {
    long long pom = 1;
    pom *= dwumian;
    pom %= MOD;
    pom *= qpow(j, n);
    pom %= MOD;
    if ((j + k) % 2) pom *= -1;
    coef += pom;
    coef %= MOD;
    dwumian *= (k - j);
    dwumian %= MOD;
    dwumian *= qpow(j + 1, MOD - 2);
    dwumian %= MOD;
  }
  long long silnia = 1;
  for (int i = 2; i <= k; i++) {
    silnia *= i;
    silnia %= MOD;
  }
  coef *= qpow(silnia, MOD - 2);
  coef %= MOD;
  return coef;
}
int main() {
  int n, k;
  cin >> n >> k;
  long long res = 0;
  long long coef = stirling(n, k) + (n - 1) * stirling(n - 1, k);
  coef %= MOD;
  for (int i = 0; i < n; i++) {
    long long w;
    cin >> w;
    res += w * coef;
    res %= MOD;
  }
  res += MOD;
  res %= MOD;
  cout << res;
}

```