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Points: 100
Time limit: 1.0s
Python 3 5.0s
Memory limit: 256M
Python 3 977M

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Problem type

After becoming CEO of Hoptiver, Andy is now a millionare! Unsure what to do with all his newfound wealth, Andy decides to buy a Bugatti like his favourite influencer.

However, in his infinite wealth Andy only owns banknotes worth multiples of million dollars. Andy wonders, with how many different combinations of his n denominations of bank notes could he buy a Bugatti of cost k million dollars.

Input Format

The input will consist of two lines. The first line has two space-separated integers, n and k. The following line consists of n integers, the ith of which represents the value of his ith type of bank note, in millions of dollars. These values will be distinct.

Output Format

The output should consist of a single integer, representing the number of combinations. Since there could be many combinations, output this value modulo 1e9+7.

Sample Input

3 5
1 2 3

Sample Output

5

Sample Explanation

The combinations that sum to 5 million dollars are 1+1+1+1+1, 1+1+1+2, 1+1+3, 1+2+2 and 2+3.

Constraints

1 \le n \le 50

1 \le a[i] \le 50. That is, the value of each bank note is between 1 and 50 million dollars.

1 \le k \le 1e5


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