#include <bits/stdc++.h>
using namespace std;
inline int read() {
  int f = 1, x = 0;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
inline long long readll() {
  long long f = 1, x = 0;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
const int MAXN = 2e5 + 5, MOD = 1e9 + 7;
inline int pow_mod(int x, int i) {
  int y = 1;
  while (i) {
    if (i & 1) y = (long long)y * x % MOD;
    x = (long long)x * x % MOD;
    i >>= 1;
  }
  return y;
}
int n, K, w[MAXN], fac[MAXN];
int main() {
  n = read();
  K = read();
  for (int i = 1; i <= n; ++i) w[i] = read();
  fac[0] = 1;
  for (int i = 1; i <= n; ++i) fac[i] = (long long)fac[i - 1] * i % MOD;
  int s1 = 0, s2 = 0;
  for (int i = 0; i <= K; ++i)
    s1 = (s1 + (long long)pow_mod(i, n) * pow_mod(MOD - 1, K - i) % MOD *
                   pow_mod(fac[i], MOD - 2) % MOD *
                   pow_mod(fac[K - i], MOD - 2) % MOD) %
         MOD;
  for (int i = 0; i <= K; ++i)
    s2 = (s2 + (long long)pow_mod(i, n - 1) * pow_mod(MOD - 1, K - i) % MOD *
                   pow_mod(fac[i], MOD - 2) % MOD *
                   pow_mod(fac[K - i], MOD - 2) % MOD) %
         MOD;
  int ans = 0;
  for (int i = 1; i <= n; ++i)
    ans = (ans + (long long)w[i] *
                     ((s1 + (long long)(n - 1) * s2 % MOD) % MOD) % MOD) %
          MOD;
  cout << ans << endl;
  return 0;
}

### Prompt

Please formulate 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>
using namespace std;
inline int read() {
  int f = 1, x = 0;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
inline long long readll() {
  long long f = 1, x = 0;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
const int MAXN = 2e5 + 5, MOD = 1e9 + 7;
inline int pow_mod(int x, int i) {
  int y = 1;
  while (i) {
    if (i & 1) y = (long long)y * x % MOD;
    x = (long long)x * x % MOD;
    i >>= 1;
  }
  return y;
}
int n, K, w[MAXN], fac[MAXN];
int main() {
  n = read();
  K = read();
  for (int i = 1; i <= n; ++i) w[i] = read();
  fac[0] = 1;
  for (int i = 1; i <= n; ++i) fac[i] = (long long)fac[i - 1] * i % MOD;
  int s1 = 0, s2 = 0;
  for (int i = 0; i <= K; ++i)
    s1 = (s1 + (long long)pow_mod(i, n) * pow_mod(MOD - 1, K - i) % MOD *
                   pow_mod(fac[i], MOD - 2) % MOD *
                   pow_mod(fac[K - i], MOD - 2) % MOD) %
         MOD;
  for (int i = 0; i <= K; ++i)
    s2 = (s2 + (long long)pow_mod(i, n - 1) * pow_mod(MOD - 1, K - i) % MOD *
                   pow_mod(fac[i], MOD - 2) % MOD *
                   pow_mod(fac[K - i], MOD - 2) % MOD) %
         MOD;
  int ans = 0;
  for (int i = 1; i <= n; ++i)
    ans = (ans + (long long)w[i] *
                     ((s1 + (long long)(n - 1) * s2 % MOD) % MOD) % MOD) %
          MOD;
  cout << ans << endl;
  return 0;
}

```