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