#include <bits/stdc++.h>
using namespace std;
namespace _GuYueNa {
inline long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') f = -1;
  for (; isdigit(ch); ch = getchar()) x = x * 10 - 48 + ch;
  return x * f;
}
inline void write(long long x) {
  if (x < 0) putchar('-'), x = -x;
  if (x >= 10) write(x / 10);
  putchar(x % 10 + '0');
}
inline void writeln(long long x) {
  write(x);
  puts("");
}
}  // namespace _GuYueNa
using namespace _GuYueNa;
const long long mod = 1e9 + 7, N = 4000010;
long long fac[N], Inv[N], n, k, cogito;
long long ppow(long long x, long long k) {
  long long ans = 1;
  for (; k; k >>= 1, ((x) = 1LL * (x) * (x) % mod))
    if (k & 1) ((ans) = 1LL * (ans) * (x) % mod);
  return ans;
}
long long C(long long n, long long k) {
  return fac[n] * Inv[k] % mod * Inv[n - k] % mod;
}
long long S(long long n, long long k) {
  if (k > n) return 0;
  long long ans = 0;
  for (long long i = 0; i <= k; ++i)
    ((ans) = ((ans) + (ppow(i, n) * C(k, i) % mod * ppow(-1, k - i))) % mod);
  return ans * Inv[k] % mod;
}
int main() {
  n = read(), k = read();
  for (long long i = 1; i <= n; ++i) cogito = (cogito + read()) % mod;
  for (long long i = 0; i <= n; ++i)
    fac[i] = i ? fac[i - 1] * i % mod : 1, Inv[i] = ppow(fac[i], mod - 2);
  long long ans = (S(n, k) + (n - 1) * S(n - 1, k)) % mod;
  ((ans) = 1LL * (ans) * (cogito) % mod);
  writeln((ans + mod) % mod);
}

### Prompt

Please provide a CPP coded solution 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;
namespace _GuYueNa {
inline long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  for (; !isdigit(ch); ch = getchar())
    if (ch == '-') f = -1;
  for (; isdigit(ch); ch = getchar()) x = x * 10 - 48 + ch;
  return x * f;
}
inline void write(long long x) {
  if (x < 0) putchar('-'), x = -x;
  if (x >= 10) write(x / 10);
  putchar(x % 10 + '0');
}
inline void writeln(long long x) {
  write(x);
  puts("");
}
}  // namespace _GuYueNa
using namespace _GuYueNa;
const long long mod = 1e9 + 7, N = 4000010;
long long fac[N], Inv[N], n, k, cogito;
long long ppow(long long x, long long k) {
  long long ans = 1;
  for (; k; k >>= 1, ((x) = 1LL * (x) * (x) % mod))
    if (k & 1) ((ans) = 1LL * (ans) * (x) % mod);
  return ans;
}
long long C(long long n, long long k) {
  return fac[n] * Inv[k] % mod * Inv[n - k] % mod;
}
long long S(long long n, long long k) {
  if (k > n) return 0;
  long long ans = 0;
  for (long long i = 0; i <= k; ++i)
    ((ans) = ((ans) + (ppow(i, n) * C(k, i) % mod * ppow(-1, k - i))) % mod);
  return ans * Inv[k] % mod;
}
int main() {
  n = read(), k = read();
  for (long long i = 1; i <= n; ++i) cogito = (cogito + read()) % mod;
  for (long long i = 0; i <= n; ++i)
    fac[i] = i ? fac[i - 1] * i % mod : 1, Inv[i] = ppow(fac[i], mod - 2);
  long long ans = (S(n, k) + (n - 1) * S(n - 1, k)) % mod;
  ((ans) = 1LL * (ans) * (cogito) % mod);
  writeln((ans + mod) % mod);
}

```