Maximum Reduction

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.

inputFormat

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.

outputFormat

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.

样例

3 2
9 1 10

29

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