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:

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

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:

8