#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T &t) {
  t = 0;
  char c = getchar();
  int f = 1;
  while (c < '0' || c > '9') {
    if (c == '-') f = -f;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    t = (t << 3) + (t << 1) + c - '0';
    c = getchar();
  }
  t *= f;
}
template <typename T, typename... Args>
inline void read(T &t, Args &...args) {
  read(t);
  read(args...);
}
template <typename T>
inline void write(T x) {
  if (x < 0) {
    x = -x;
    putchar('-');
  }
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
}
int n, k, w[200005], fac[200005], ifac[200005];
int mul(int a, int b) { return 1ll * a * b % 1000000007; }
int dec(int a, int b) { return a >= b ? a - b : a + 1000000007 - b; }
int add(int a, int b) {
  return a + b >= 1000000007 ? a + b - 1000000007 : a + b;
}
int binom(int a, int b) {
  return a >= b ? mul(fac[a], mul(ifac[b], ifac[a - b])) : 0;
}
int qkpow(int a, int b) {
  int res = 1;
  for (; b; b >>= 1, a = mul(a, a))
    if (b & 1) res = mul(res, a) % 1000000007;
  return res;
}
int Sitelin(int n, int m) {
  int res = 0;
  for (register int i = 0, tmp; i <= m; ++i)
    tmp = mul(binom(m, i), qkpow(i, n)),
    m - i & 1 ? (res = dec(res, tmp)) : (res = add(res, tmp));
  return 1ll * res * ifac[m] % 1000000007;
}
signed main() {
  read(n, k);
  fac[0] = 1;
  int sum = 0;
  for (register int i = 1; i <= n; ++i) read(w[i]), sum = add(sum, w[i]);
  for (register int i = 1; i <= k; ++i) fac[i] = mul(fac[i - 1], i);
  ifac[k] = qkpow(fac[k], 1000000007 - 2);
  for (register int i = k; i; --i) ifac[i - 1] = mul(ifac[i], i);
  write(mul(sum, add(Sitelin(n, k), mul(n - 1, Sitelin(n - 1, k))))),
      putchar('\n');
  return 0;
}

### Prompt

Generate 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>
inline void read(T &t) {
  t = 0;
  char c = getchar();
  int f = 1;
  while (c < '0' || c > '9') {
    if (c == '-') f = -f;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    t = (t << 3) + (t << 1) + c - '0';
    c = getchar();
  }
  t *= f;
}
template <typename T, typename... Args>
inline void read(T &t, Args &...args) {
  read(t);
  read(args...);
}
template <typename T>
inline void write(T x) {
  if (x < 0) {
    x = -x;
    putchar('-');
  }
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
}
int n, k, w[200005], fac[200005], ifac[200005];
int mul(int a, int b) { return 1ll * a * b % 1000000007; }
int dec(int a, int b) { return a >= b ? a - b : a + 1000000007 - b; }
int add(int a, int b) {
  return a + b >= 1000000007 ? a + b - 1000000007 : a + b;
}
int binom(int a, int b) {
  return a >= b ? mul(fac[a], mul(ifac[b], ifac[a - b])) : 0;
}
int qkpow(int a, int b) {
  int res = 1;
  for (; b; b >>= 1, a = mul(a, a))
    if (b & 1) res = mul(res, a) % 1000000007;
  return res;
}
int Sitelin(int n, int m) {
  int res = 0;
  for (register int i = 0, tmp; i <= m; ++i)
    tmp = mul(binom(m, i), qkpow(i, n)),
    m - i & 1 ? (res = dec(res, tmp)) : (res = add(res, tmp));
  return 1ll * res * ifac[m] % 1000000007;
}
signed main() {
  read(n, k);
  fac[0] = 1;
  int sum = 0;
  for (register int i = 1; i <= n; ++i) read(w[i]), sum = add(sum, w[i]);
  for (register int i = 1; i <= k; ++i) fac[i] = mul(fac[i - 1], i);
  ifac[k] = qkpow(fac[k], 1000000007 - 2);
  for (register int i = k; i; --i) ifac[i - 1] = mul(ifac[i], i);
  write(mul(sum, add(Sitelin(n, k), mul(n - 1, Sitelin(n - 1, k))))),
      putchar('\n');
  return 0;
}

```