#include <bits/stdc++.h>
using namespace std;
static const int mod = 1000000007;
int qp(int a, int b) {
  long long p = 1, q = a;
  while (b) {
    if (b & 1) p = p * q % mod;
    q = q * q % mod;
    b >>= 1;
  }
  return p;
}
int c(int n, int k, const vector<int> &f, const vector<int> &rf) {
  return 1LL * rf[k] * rf[n - k] % mod * f[n] % mod;
}
int sterling(int n, int k, const vector<int> &f, const vector<int> &rf) {
  int s = 0;
  for (int i = 1; i <= k; ++i)
    if ((i + k) & 1)
      s = (s - 1LL * c(k, i, f, rf) * qp(i, n) % mod + mod) % mod;
    else
      s = (s + 1LL * c(k, i, f, rf) * qp(i, n) % mod) % mod;
  return 1LL * s * rf[k] % mod;
}
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  int s = 0;
  for (int i = 0; i < n; ++i) {
    int w;
    scanf("%d", &w);
    s = (s + w) % mod;
  }
  if (k == 1)
    cout << 1LL * s * n % mod << endl;
  else {
    vector<int> f(n + 1), rf(n + 1);
    f[0] = rf[0] = 1;
    for (int i = 1; i <= n; ++i) {
      f[i] = 1LL * f[i - 1] * i % mod;
      rf[i] = qp(f[i], mod - 2);
    }
    int ans = (sterling(n, k, f, rf) +
               1LL * (n - 1) * sterling(n - 1, k, f, rf) % mod) %
              mod;
    ans = 1LL * s * ans % mod;
    printf("%d\n", ans);
  }
  return 0;
}

### 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;
static const int mod = 1000000007;
int qp(int a, int b) {
  long long p = 1, q = a;
  while (b) {
    if (b & 1) p = p * q % mod;
    q = q * q % mod;
    b >>= 1;
  }
  return p;
}
int c(int n, int k, const vector<int> &f, const vector<int> &rf) {
  return 1LL * rf[k] * rf[n - k] % mod * f[n] % mod;
}
int sterling(int n, int k, const vector<int> &f, const vector<int> &rf) {
  int s = 0;
  for (int i = 1; i <= k; ++i)
    if ((i + k) & 1)
      s = (s - 1LL * c(k, i, f, rf) * qp(i, n) % mod + mod) % mod;
    else
      s = (s + 1LL * c(k, i, f, rf) * qp(i, n) % mod) % mod;
  return 1LL * s * rf[k] % mod;
}
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  int s = 0;
  for (int i = 0; i < n; ++i) {
    int w;
    scanf("%d", &w);
    s = (s + w) % mod;
  }
  if (k == 1)
    cout << 1LL * s * n % mod << endl;
  else {
    vector<int> f(n + 1), rf(n + 1);
    f[0] = rf[0] = 1;
    for (int i = 1; i <= n; ++i) {
      f[i] = 1LL * f[i - 1] * i % mod;
      rf[i] = qp(f[i], mod - 2);
    }
    int ans = (sterling(n, k, f, rf) +
               1LL * (n - 1) * sterling(n - 1, k, f, rf) % mod) %
              mod;
    ans = 1LL * s * ans % mod;
    printf("%d\n", ans);
  }
  return 0;
}

```