Currency System

Problem Description

You are given a currency system with $n$ denominations. Compute the number of ways to make up an amount of face value $m$ using these denominations.

Input Format

The first line contains two integers $n$ and $m$ $(1\le n\le 20,\ 1\le m\le 4000)$.

The following $n$ lines each contain one integer, the face value of one denomination.

Output Format

Output a single integer: the number of ways to compose currency of face value $m$.

Sample Input

3 10
1
2
5

Sample Output

10

Constraints

$1\le n\le 20$, $1\le m\le 4000$. Time limit 1s, memory limit 1024KiB for each test case.