#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
struct state_t {
  long long total = 0LL;
  stack<pair<int, int>, vector<pair<int, int>>> blocks;
};
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  vector<int> values(n);
  for (int i = 0; i < n; ++i) scanf("%d", &values[i]);
  vector<int> max_left(n), max_right(n);
  for (int i = 0; i < n; ++i)
    if (i % (k - 1) == 0)
      max_left[i] = values[i];
    else
      max_left[i] = max(values[i], max_left[i - 1]);
  for (int i = n - 1; i >= 0; --i)
    if (i == n - 1 || (i + 1) % (k - 1) == 0)
      max_right[i] = values[i];
    else
      max_right[i] = max(values[i], max_right[i + 1]);
  vector<state_t> states(k);
  int result = 0;
  for (int i = n - 1; i >= 0; --i) {
    int end = i + k - 1;
    if (end >= n) {
      continue;
    }
    state_t &st = states[i % (k - 1)];
    int rv = max(max_right[i], max_left[end]);
    int size = 1;
    while (!st.blocks.empty() && st.blocks.top().first <= rv) {
      st.total -= (long long)st.blocks.top().first * st.blocks.top().second;
      size += st.blocks.top().second;
      st.blocks.pop();
    }
    st.blocks.emplace(rv, size);
    st.total += (long long)rv * size;
    result = ((long long)result + st.total) % mod;
  }
  printf("%d\n", result);
  return 0;
}

### Prompt

Your challenge is to write a Cpp solution 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 mod = 1e9 + 7;
struct state_t {
  long long total = 0LL;
  stack<pair<int, int>, vector<pair<int, int>>> blocks;
};
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  vector<int> values(n);
  for (int i = 0; i < n; ++i) scanf("%d", &values[i]);
  vector<int> max_left(n), max_right(n);
  for (int i = 0; i < n; ++i)
    if (i % (k - 1) == 0)
      max_left[i] = values[i];
    else
      max_left[i] = max(values[i], max_left[i - 1]);
  for (int i = n - 1; i >= 0; --i)
    if (i == n - 1 || (i + 1) % (k - 1) == 0)
      max_right[i] = values[i];
    else
      max_right[i] = max(values[i], max_right[i + 1]);
  vector<state_t> states(k);
  int result = 0;
  for (int i = n - 1; i >= 0; --i) {
    int end = i + k - 1;
    if (end >= n) {
      continue;
    }
    state_t &st = states[i % (k - 1)];
    int rv = max(max_right[i], max_left[end]);
    int size = 1;
    while (!st.blocks.empty() && st.blocks.top().first <= rv) {
      st.total -= (long long)st.blocks.top().first * st.blocks.top().second;
      size += st.blocks.top().second;
      st.blocks.pop();
    }
    st.blocks.emplace(rv, size);
    st.total += (long long)rv * size;
    result = ((long long)result + st.total) % mod;
  }
  printf("%d\n", result);
  return 0;
}

```