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CSES Problem Set

Coin Combinations II


Task | Statistics


CSES - Coin Combinations IICSES - Coin Combinations II

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 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: 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
Example

Input:
3 9
2 3 5


Output:
3