#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T &x) {
  register int c = getchar();
  x = 0;
  bool f = 0;
  for (; !isdigit(c); c = getchar()) f ^= !(c ^ 45);
  for (; isdigit(c); c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
  if (f) x = -x;
}
template <typename T, typename... Args>
inline void read(T &x, Args &...args) {
  read(x);
  read(args...);
}
template <typename T>
inline void write(T x) {
  static int sta[35];
  register int top = 0;
  if (x < 0) x = -x, putchar('-');
  do {
    sta[top++] = x % 10, x /= 10;
  } while (x);
  while (top) putchar(sta[--top] + '0');
}
template <typename T>
inline void write(T x, const char &c) {
  write(x), putchar(c);
}
const int N = 2e5 + 20, P = 1e9 + 7;
int n, k;
long long w, ans, p, fact[N];
inline void init(int m) {
  fact[0] = 1;
  for (register int i = 1; i <= m; i++) {
    fact[i] = fact[i - 1] * i % P;
  }
}
inline long long qPow(long long a, long long b) {
  long long ret = 1;
  while (b) {
    if (b & 1) (ret *= a) %= P;
    (a *= a) %= P;
    b >>= 1;
  }
  return ret;
}
inline long long inv(long long a) { return qPow(a, P - 2); }
int main() {
  read(n, k);
  init(n);
  for (register int i = 0; i <= k; i++) {
    (p += ((i & 1) ? P - 1 : 1) * fact[k] % P * inv(fact[i] * fact[k - i] % P) %
          P * (qPow(k - i, n) + qPow(k - i, n - 1) * (n - 1) % P) % P) %= P;
  }
  (p *= inv(fact[k])) %= P;
  for (register int i = 1; i <= n; i++) {
    read(w);
    (ans += p * w % P) %= P;
  }
  write(ans, '\n');
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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 &x) {
  register int c = getchar();
  x = 0;
  bool f = 0;
  for (; !isdigit(c); c = getchar()) f ^= !(c ^ 45);
  for (; isdigit(c); c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
  if (f) x = -x;
}
template <typename T, typename... Args>
inline void read(T &x, Args &...args) {
  read(x);
  read(args...);
}
template <typename T>
inline void write(T x) {
  static int sta[35];
  register int top = 0;
  if (x < 0) x = -x, putchar('-');
  do {
    sta[top++] = x % 10, x /= 10;
  } while (x);
  while (top) putchar(sta[--top] + '0');
}
template <typename T>
inline void write(T x, const char &c) {
  write(x), putchar(c);
}
const int N = 2e5 + 20, P = 1e9 + 7;
int n, k;
long long w, ans, p, fact[N];
inline void init(int m) {
  fact[0] = 1;
  for (register int i = 1; i <= m; i++) {
    fact[i] = fact[i - 1] * i % P;
  }
}
inline long long qPow(long long a, long long b) {
  long long ret = 1;
  while (b) {
    if (b & 1) (ret *= a) %= P;
    (a *= a) %= P;
    b >>= 1;
  }
  return ret;
}
inline long long inv(long long a) { return qPow(a, P - 2); }
int main() {
  read(n, k);
  init(n);
  for (register int i = 0; i <= k; i++) {
    (p += ((i & 1) ? P - 1 : 1) * fact[k] % P * inv(fact[i] * fact[k - i] % P) %
          P * (qPow(k - i, n) + qPow(k - i, n - 1) * (n - 1) % P) % P) %= P;
  }
  (p *= inv(fact[k])) %= P;
  for (register int i = 1; i <= n; i++) {
    read(w);
    (ans += p * w % P) %= P;
  }
  write(ans, '\n');
  return 0;
}

```