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. 
#include <bits/stdc++.h>
using namespace std;
const int maxn = 202020;
const int mod = 1000000007;
int a[maxn], s;
int fac[maxn], ifac[maxn];
int qpow(int a, int n) {
  int ans = 1;
  for (; n; n >>= 1, a = (long long)a * a % mod)
    if (n & 1) ans = (long long)ans * a % mod;
  return ans;
}
int gets(int n, int m) {
  if (m > n) return 0;
  int ans = 0;
  for (int i = 0; i <= m; i++) {
    if (i % 2 == 0)
      ans = (ans + (long long)fac[m] * ifac[i] % mod * ifac[m - i] % mod *
                       qpow(m - i, n) % mod) %
            mod;
    else
      ans = (ans -
             (long long)fac[m] * ifac[i] % mod * ifac[m - i] % mod *
                 qpow(m - i, n) % mod +
             mod) %
            mod;
  }
  return ans * (long long)ifac[m] % mod;
}
int main(void) {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]), s = (s + a[i]) % mod;
  fac[0] = 1;
  for (int i = 1; i <= k; i++) fac[i] = fac[i - 1] * (long long)i % mod;
  ifac[k] = qpow(fac[k], mod - 2);
  for (int i = k - 1; i >= 0; i--)
    ifac[i] = ifac[i + 1] * (long long)(i + 1) % mod;
  int ans = (gets(n, k) + (long long)gets(n - 1, k) * (n - 1)) % mod;
  printf("%I64d\n", ans * (long long)s % mod);
  return 0;
}
