Consider a money system consisting of $n$ coins. Each coin has a positive integer value. Your task is to calculate the number of distinct 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 $8$ ways:

• $2+2+5$
• $2+5+2$
• $5+2+2$
• $3+3+3$
• $2+2+2+3$
• $2+2+3+2$
• $2+3+2+2$
• $3+2+2+2$

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.

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

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