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 Specification

• 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 Specification

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

Constrains

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

Sample Cases

Input #1:

3 9
2 3 5

Output #1:

3