With Christmas approaching, AQT is making preparations. He has purchased a row of ~N~ lights to put on his Christmas tree, the ~i^{th}~ light having a brightness value of ~a_i~. AQT can control which lights are on/off and would like the brightness level of the tree (calculated by taking the average of the brightness values of lights that are on) to be exactly ~K~.

How many ways can he achieve this? Since this value can be quite large, find the answer modulo ~10^9+7~.

Input Specification

The first line contains two integers ~N~ and ~K~ ~(1 \leq N,K \leq 500)~

The second line contains ~N~ space separated integers, ~a_1,a_2,\dots,a_N~ ~(0 \leq a_i \leq 500)~

Output Specification

Output a single integer, the number of ways AQT can select lights to attain the target brightness level modulo ~10^9+7~.

Subtasks

Subtask 1 [10%]

~1 \leq N,K,a_i \le 10~

Subtask 2 [40%]

~1 \leq N,K,a_i \le 50~

Subtask 3 [50%]

No further constraints.

Sample Input

4 3
3 2 4 3

Sample Output

7

Sample Explanation

AQT can pick the following ~7~ combinations of lights (indices are shown intstead of value): ~(1)~, ~(4)~, ~(2,3)~, ~(1,4)~, ~(1,2,3)~, ~(2,3,4)~, ~(1,2,3,4)~.