Subsets with Fixed Average

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