Consider a money system consisting of n coins. Each coin has a positive integer value. Your task is to calculate the number of distinct ordered ways you can produce a money sum x using the available coins.

For example, if the coins are \{2,3,5\} and the desired sum is 9, there are 3 ways:

• 2+2+5
• 3+3+3
• 2+2+2+3

Input

The first input line has two integers n and x: the number of coins and the desired sum of money.

The second line has n distinct integers c_1,c_2,\dots,c_n: the value of each coin.

Output

Print one integer: the number of ways modulo 10^9+7.

Constraints

• 1 \le n \le 100
• 1 \le x \le 10^6
• 1 \le c_i \le 10^6

Example

Input:

3 9
2 3 5

Output:

3