The value of an array $B$ is the maximum element in $B$.
Given an array $A$ of $n$ integers. Find the sum of value of all subsequences of length $k$ of $A$.
### Input
- The first line contains 2 integers $n, k$.
- The second line contains $n$ integers $A_i$.
### Output
- Print the sum, modulo $10^9+7$.
### Constraints
- $1 \le k \le n \le 10^5$.
### Example
Input:
```
4 2
6 7 6 5
```
Output:
```
39
```