#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1000005;
inline int readint() {
  int res = 0, f = 1;
  char c = 0;
  while (!isdigit(c)) {
    c = getchar();
    if (c == '-') f = -1;
  }
  while (isdigit(c)) res = res * 10 + c - '0', c = getchar();
  return res * f;
}
int n, k, a[MAXN];
int stc[MAXN], nxt[MAXN], lst[MAXN], top;
inline int calc(int len) {
  int t = len / (k - 1);
  if (t == 0) return 0;
  long long res = 1ll *
                  (2 * len - 2 * k + 2 - 1ll * (t - 1) * (k - 1) % 1000000007) *
                  t / 2;
  return res % 1000000007;
}
int main() {
  n = readint(), k = readint();
  for (int i = 1; i <= n; i++) a[i] = readint();
  for (int i = 1; i <= n; i++) {
    while (top && a[stc[top]] <= a[i]) nxt[stc[top]] = i, top--;
    lst[i] = stc[top], stc[++top] = i;
  }
  for (int i = 1; i <= top; i++) nxt[stc[i]] = n + 1;
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    int l = lst[i], r = nxt[i];
    int tmp = calc(r - l - 1) - calc(i - l - 1) - calc(r - i - 1);
    tmp = (tmp % 1000000007 + 1000000007) % 1000000007;
    ans = (ans + 1ll * a[i] * tmp) % 1000000007;
  }
  printf("%d\n", ans);
  return 0;
}

### Prompt

Please create a solution in cpp to the following problem:

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>
using namespace std;
const int MAXN = 1000005;
inline int readint() {
  int res = 0, f = 1;
  char c = 0;
  while (!isdigit(c)) {
    c = getchar();
    if (c == '-') f = -1;
  }
  while (isdigit(c)) res = res * 10 + c - '0', c = getchar();
  return res * f;
}
int n, k, a[MAXN];
int stc[MAXN], nxt[MAXN], lst[MAXN], top;
inline int calc(int len) {
  int t = len / (k - 1);
  if (t == 0) return 0;
  long long res = 1ll *
                  (2 * len - 2 * k + 2 - 1ll * (t - 1) * (k - 1) % 1000000007) *
                  t / 2;
  return res % 1000000007;
}
int main() {
  n = readint(), k = readint();
  for (int i = 1; i <= n; i++) a[i] = readint();
  for (int i = 1; i <= n; i++) {
    while (top && a[stc[top]] <= a[i]) nxt[stc[top]] = i, top--;
    lst[i] = stc[top], stc[++top] = i;
  }
  for (int i = 1; i <= top; i++) nxt[stc[i]] = n + 1;
  int ans = 0;
  for (int i = 1; i <= n; i++) {
    int l = lst[i], r = nxt[i];
    int tmp = calc(r - l - 1) - calc(i - l - 1) - calc(r - i - 1);
    tmp = (tmp % 1000000007 + 1000000007) % 1000000007;
    ans = (ans + 1ll * a[i] * tmp) % 1000000007;
  }
  printf("%d\n", ans);
  return 0;
}

```