Tak and Cards

Tak has N cards. On the i-th (1 \leq i \leq N) card is written an integer x_i. He is selecting one or more cards from these N cards, so that the average of the integers written on the selected cards is exactly A. In how many ways can he make his selection?

Constraints

• 1 \leq N \leq 50
• 1 \leq A \leq 50
• 1 \leq x_i \leq 50
• N,,A,,x_i are integers.

Input

The input is given from Standard Input in the following format:

N A x_1 x_2 ... x_N

Output

Print the number of ways to select cards such that the average of the written integers is exactly A.

Examples

Input

4 8 7 9 8 9

Output

5

Input

3 8 6 6 9

Output

0

Input

8 5 3 6 2 8 7 6 5 9

Output

19

Input

33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Output

8589934591

inputFormat

Input

The input is given from Standard Input in the following format:

N A x_1 x_2 ... x_N

outputFormat

Output

Print the number of ways to select cards such that the average of the written integers is exactly A.

Examples

Input

4 8 7 9 8 9

Output

5

Input

3 8 6 6 9

Output

0

Input

8 5 3 6 2 8 7 6 5 9

Output

19

Input

33 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Output

8589934591

样例

4 8
7 9 8 9

5