#include <bits/stdc++.h>
using ll = long long;
const int M = 1000000007, C = 200001;
inline ll pow(ll a, ll b, ll M) {
  if (b == 0) return 1;
  ll c = 1;
  while (b > 0) {
    if (b % 2 == 1) c = (c * a) % M;
    b /= 2;
    a = (a * a) % M;
  }
  return c;
}
ll fac[C], af[C];
void formulate_fac(int n) {
  int i;
  fac[0] = af[0] = 1;
  for (i = 1; i < n; i++) fac[i] = (i * fac[i - 1]) % M;
  for (i = 1; i < n; i++) af[i] = (pow(i, M - 2, M) * af[i - 1]) % M;
}
inline ll cn(int n, int k) {
  if (n < k || n < 0 || k < 0) return 0;
  return (((fac[n] * af[k]) % M) * af[n - k]) % M;
}
ll calc_stirling2(ll n, ll k, ll M) {
  ll sgn = 1, res = 0, i;
  for (i = 0; i <= k; i++) {
    res = (res + sgn * cn(k, i) * pow(k - i, n, M)) % M;
    sgn *= (-1);
  }
  return (res * af[k]) % M;
}
int main() {
  ll w, n, k, res = 0, sum_w = 0;
  int i;
  formulate_fac(C);
  scanf("%lld %lld", &n, &k);
  for (i = 0; i < n; i++) scanf("%lld", &w), sum_w += w;
  res = ((n - 1) * calc_stirling2(n - 1, k, M) + calc_stirling2(n, k, M)) % M;
  res = (res * (sum_w % M)) % M;
  if (res < 0) res += M;
  printf("%lld\n", res);
  return 0;
}

### Prompt

Create a solution in CPP for 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 ll = long long;
const int M = 1000000007, C = 200001;
inline ll pow(ll a, ll b, ll M) {
  if (b == 0) return 1;
  ll c = 1;
  while (b > 0) {
    if (b % 2 == 1) c = (c * a) % M;
    b /= 2;
    a = (a * a) % M;
  }
  return c;
}
ll fac[C], af[C];
void formulate_fac(int n) {
  int i;
  fac[0] = af[0] = 1;
  for (i = 1; i < n; i++) fac[i] = (i * fac[i - 1]) % M;
  for (i = 1; i < n; i++) af[i] = (pow(i, M - 2, M) * af[i - 1]) % M;
}
inline ll cn(int n, int k) {
  if (n < k || n < 0 || k < 0) return 0;
  return (((fac[n] * af[k]) % M) * af[n - k]) % M;
}
ll calc_stirling2(ll n, ll k, ll M) {
  ll sgn = 1, res = 0, i;
  for (i = 0; i <= k; i++) {
    res = (res + sgn * cn(k, i) * pow(k - i, n, M)) % M;
    sgn *= (-1);
  }
  return (res * af[k]) % M;
}
int main() {
  ll w, n, k, res = 0, sum_w = 0;
  int i;
  formulate_fac(C);
  scanf("%lld %lld", &n, &k);
  for (i = 0; i < n; i++) scanf("%lld", &w), sum_w += w;
  res = ((n - 1) * calc_stirling2(n - 1, k, M) + calc_stirling2(n, k, M)) % M;
  res = (res * (sum_w % M)) % M;
  if (res < 0) res += M;
  printf("%lld\n", res);
  return 0;
}

```