**Time limit:**1.00 s**Memory limit:**512 MB

You are given an array of n numbers. In how many ways can you choose a subset of the numbers with sum x?

# Input

The first input line has two numbers n and x: the array size and the required sum.

The second line has n integers t_1,t_2,\dots,t_n: the numbers in the array.

# Output

Print the number of ways you can create the sum x.

# Constraints

- 1 \le n \le 40
- 1 \le x \le 10^9
- 1 \le t_i \le 10^9

# Example

Input:

4 5 1 2 3 2

Output:

3