- Time limit: 1.00 s
- Memory limit: 512 MB
You are given an array of n integers. Your task is to count the number of non-empty subsets of the given array with average equal to a.
Input
The first line has two integers n and a: the size of the array and the target average.
The next line has n integers x_1, x_2,\dots, x_n: the contents of the array.
Output
Print one integer: the number of non-empty subsets with average equal to a, modulo 10^9 + 7.
Constraints
- 1 \le n \le 500
- 1 \le a \le 500
- 1 \le x_i \le 500
Example
Input:
5 2 1 1 2 3 4
Output:
7