Meet in the Middle

• 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