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**Task** | Statistics

Time limit: | 1.00 s | Memory limit: | 512 MB |

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.

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

- $1 \le n \le 100$

- $1 \le x \le 10^6$

- $1 \le c_i \le 10^6$

Input:

`3 9`

2 3 5

Output:

`8`