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

Example Output

3