#include <bits/stdc++.h>
using namespace std;
const int _ = 2e5 + 5, yl = 1e9 + 7;
long long n, k, sum, mul[_], inv[_];
void inc(long long &x, long long y) {
  x += y;
  if (x >= yl) x -= yl;
}
void dec(long long &x, long long y) {
  x -= y;
  if (x < 0) x += yl;
}
long long POW(long long x, long long y) {
  long long res = 1;
  while (y) {
    if (y & 1) res = res * x % yl;
    x = x * x % yl;
    y >>= 1;
  }
  return res;
}
long long S(int x, int y) {
  long long res = 0;
  for (int i = 0; i <= y; ++i)
    if (i & 1)
      dec(res, POW(y - i, x) * inv[i] % yl * inv[y - i] % yl);
    else
      inc(res, POW(y - i, x) * inv[i] % yl * inv[y - i] % yl);
  return res;
}
int main() {
  cin >> n >> k;
  inv[0] = inv[1] = mul[0] = 1;
  for (int i = 2; i <= n; ++i) inv[i] = (yl - yl / i) * inv[yl % i] % yl;
  for (int i = 1; i <= n; ++i)
    mul[i] = mul[i - 1] * i % yl, inv[i] = inv[i] * inv[i - 1] % yl;
  for (int i = 1, x; i <= n; ++i) cin >> x, sum += x;
  cout << sum % yl * (S(n, k) + (n - 1) * S(n - 1, k) % yl) % yl << endl;
}

### Prompt

Your challenge is to write 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;
const int _ = 2e5 + 5, yl = 1e9 + 7;
long long n, k, sum, mul[_], inv[_];
void inc(long long &x, long long y) {
  x += y;
  if (x >= yl) x -= yl;
}
void dec(long long &x, long long y) {
  x -= y;
  if (x < 0) x += yl;
}
long long POW(long long x, long long y) {
  long long res = 1;
  while (y) {
    if (y & 1) res = res * x % yl;
    x = x * x % yl;
    y >>= 1;
  }
  return res;
}
long long S(int x, int y) {
  long long res = 0;
  for (int i = 0; i <= y; ++i)
    if (i & 1)
      dec(res, POW(y - i, x) * inv[i] % yl * inv[y - i] % yl);
    else
      inc(res, POW(y - i, x) * inv[i] % yl * inv[y - i] % yl);
  return res;
}
int main() {
  cin >> n >> k;
  inv[0] = inv[1] = mul[0] = 1;
  for (int i = 2; i <= n; ++i) inv[i] = (yl - yl / i) * inv[yl % i] % yl;
  for (int i = 1; i <= n; ++i)
    mul[i] = mul[i - 1] * i % yl, inv[i] = inv[i] * inv[i - 1] % yl;
  for (int i = 1, x; i <= n; ++i) cin >> x, sum += x;
  cout << sum % yl * (S(n, k) + (n - 1) * S(n - 1, k) % yl) % yl << endl;
}

```