#include <bits/stdc++.h>
const int maxn = 1E6 + 77;
const int mod = 1E9 + 7;
int N, K, A[maxn], L[maxn], R[maxn], X[maxn];
bool cmp(int a, int b) { return A[a] < A[b]; }
int ans;
void update_ans(int a, int b, int p) {
  int ret = 0;
  long long t;
  if (a > b) std::swap(a, b);
  int ia = (a - 1) / (K - 1), ib = (b - 1) / (K - 1),
      ic = (a + b - 1) / (K - 1);
  ret += ia;
  if (ret >= mod) ret -= mod;
  t = (ia * (ia + 1ll) / 2) % mod;
  t = t * (K - 1) % mod;
  ret += t;
  if (ret >= mod) ret -= mod;
  ret += a * (long long)(ib - ia) % mod;
  if (ret >= mod) ret -= mod;
  ret += (a + b) * (long long)(ic - ib) % mod;
  if (ret >= mod) ret -= mod;
  ret -= (((ib + ic + 1ll) * (K - 1) + 2) * (ic - ib) / 2) % mod;
  if (ret < 0) ret += mod;
  ans += ret * (long long)A[p] % mod;
  if (ans >= mod) ans -= mod;
}
int main() {
  scanf("%d%d", &N, &K);
  for (int i = 1; i <= N; ++i) {
    scanf("%d", A + i);
    X[i] = i;
  }
  std::sort(X + 1, X + N + 1, cmp);
  for (int i = 1; i <= N; ++i) {
    int p = X[i], l = p, r = p;
    if (L[p - 1]) l = L[p - 1];
    if (R[p + 1]) r = R[p + 1];
    L[l] = L[r] = l;
    R[l] = R[r] = r;
    update_ans(p - l + 1, r - p + 1, p);
  }
  printf("%d\n", ans);
}

### Prompt

Develop a solution in Cpp to the problem described below:

Given an array a of n integers and an integer k (2 ≤ k ≤ n), where each element of the array is denoted by a_i (0 ≤ i < n). Perform the operation z given below on a and print the value of z(a,k) modulo 10^{9}+7.
    
    
      
    function z(array a, integer k):  
        if length(a) < k:  
            return 0  
        else:  
            b = empty array  
            ans = 0  
            for i = 0 .. (length(a) - k):  
                temp = a[i]  
                for j = i .. (i + k - 1):  
                    temp = max(temp, a[j])  
                append temp to the end of b  
                ans = ans + temp  
            return ans + z(b, k)  
    

Input

The first line of input contains two integers n and k (2 ≤ k ≤ n ≤ 10^6) — the length of the initial array a and the parameter k.

The second line of input contains n integers a_0, a_1, …, a_{n - 1} (1 ≤ a_{i} ≤ 10^9) — the elements of the array a.

Output

Output the only integer, the value of z(a,k) modulo 10^9+7.

Examples

Input

3 2
9 1 10


Output

29


Input

5 3
5 8 7 1 9


Output

34

Note

In the first example: 

  * for a=(9,1,10), ans=19 and b=(9,10), 
  * for a=(9,10), ans=10 and b=(10), 
  * for a=(10), ans=0. 



So the returned value is 19+10+0=29.

In the second example: 

  * for a=(5,8,7,1,9), ans=25 and b=(8,8,9), 
  * for a=(8,8,9), ans=9 and b=(9), 
  * for a=(9), ans=0. 



So the returned value is 25+9+0=34.

### Response

```cpp
#include <bits/stdc++.h>
const int maxn = 1E6 + 77;
const int mod = 1E9 + 7;
int N, K, A[maxn], L[maxn], R[maxn], X[maxn];
bool cmp(int a, int b) { return A[a] < A[b]; }
int ans;
void update_ans(int a, int b, int p) {
  int ret = 0;
  long long t;
  if (a > b) std::swap(a, b);
  int ia = (a - 1) / (K - 1), ib = (b - 1) / (K - 1),
      ic = (a + b - 1) / (K - 1);
  ret += ia;
  if (ret >= mod) ret -= mod;
  t = (ia * (ia + 1ll) / 2) % mod;
  t = t * (K - 1) % mod;
  ret += t;
  if (ret >= mod) ret -= mod;
  ret += a * (long long)(ib - ia) % mod;
  if (ret >= mod) ret -= mod;
  ret += (a + b) * (long long)(ic - ib) % mod;
  if (ret >= mod) ret -= mod;
  ret -= (((ib + ic + 1ll) * (K - 1) + 2) * (ic - ib) / 2) % mod;
  if (ret < 0) ret += mod;
  ans += ret * (long long)A[p] % mod;
  if (ans >= mod) ans -= mod;
}
int main() {
  scanf("%d%d", &N, &K);
  for (int i = 1; i <= N; ++i) {
    scanf("%d", A + i);
    X[i] = i;
  }
  std::sort(X + 1, X + N + 1, cmp);
  for (int i = 1; i <= N; ++i) {
    int p = X[i], l = p, r = p;
    if (L[p - 1]) l = L[p - 1];
    if (R[p + 1]) r = R[p + 1];
    L[l] = L[r] = l;
    R[l] = R[r] = r;
    update_ans(p - l + 1, r - p + 1, p);
  }
  printf("%d\n", ans);
}

```