#include <bits/stdc++.h>
using namespace std;
template <typename T>
void dbg(T a) {}
template <typename T, typename... Arg>
void dbg(T a, Arg... arg) {}
const int maxn = (2e5) + 7;
const int maxlog = 20;
const int inf = (1e9) + 7;
const long long LLinf = (1e18) + 7;
const long double eps = 1e-9;
const long long mod = 1e9 + 7;
long long sil[maxn], odwsil[maxn];
long long pot(long long a, long long w) {
  if (w == 0) return 1;
  long long b = pot(a, w / 2);
  b *= b;
  b %= mod;
  if (w & 1) b = (b * a) % mod;
  return b;
}
long long net(int n, int k) {
  long long res = sil[n];
  res = (res * odwsil[k]) % mod;
  res = (res * odwsil[n - k]) % mod;
  return res;
}
int s(int n, int k) {
  long long res = 0LL;
  for (int j = 0; j <= k; j++) {
    res = (res + ((pot(-1, (j ^ k) & 1) * net(k, j)) % mod) * pot(j, n)) % mod;
  }
  res = (res * odwsil[k]) % mod;
  return res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  sil[0] = 1;
  for (int i = 1; i < maxn; i++) sil[i] = (sil[i - 1] * (long long)i) % mod;
  for (int i = 0; i < maxn; i++) odwsil[i] = pot(sil[i], mod - 2);
  int n, k;
  cin >> n >> k;
  long long suma = 0LL;
  for (int i = 0; i < n; i++) {
    long long a;
    cin >> a;
    suma += a;
  }
  suma %= mod;
  suma *= (s(n, k) + (n - 1) * (long long)s(n - 1, k)) % mod;
  suma %= mod;
  suma = (suma + mod) % mod;
  cout << suma;
  return 0;
}

### Prompt

Your task is to create 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;
template <typename T>
void dbg(T a) {}
template <typename T, typename... Arg>
void dbg(T a, Arg... arg) {}
const int maxn = (2e5) + 7;
const int maxlog = 20;
const int inf = (1e9) + 7;
const long long LLinf = (1e18) + 7;
const long double eps = 1e-9;
const long long mod = 1e9 + 7;
long long sil[maxn], odwsil[maxn];
long long pot(long long a, long long w) {
  if (w == 0) return 1;
  long long b = pot(a, w / 2);
  b *= b;
  b %= mod;
  if (w & 1) b = (b * a) % mod;
  return b;
}
long long net(int n, int k) {
  long long res = sil[n];
  res = (res * odwsil[k]) % mod;
  res = (res * odwsil[n - k]) % mod;
  return res;
}
int s(int n, int k) {
  long long res = 0LL;
  for (int j = 0; j <= k; j++) {
    res = (res + ((pot(-1, (j ^ k) & 1) * net(k, j)) % mod) * pot(j, n)) % mod;
  }
  res = (res * odwsil[k]) % mod;
  return res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  sil[0] = 1;
  for (int i = 1; i < maxn; i++) sil[i] = (sil[i - 1] * (long long)i) % mod;
  for (int i = 0; i < maxn; i++) odwsil[i] = pot(sil[i], mod - 2);
  int n, k;
  cin >> n >> k;
  long long suma = 0LL;
  for (int i = 0; i < n; i++) {
    long long a;
    cin >> a;
    suma += a;
  }
  suma %= mod;
  suma *= (s(n, k) + (n - 1) * (long long)s(n - 1, k)) % mod;
  suma %= mod;
  suma = (suma + mod) % mod;
  cout << suma;
  return 0;
}

```