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### Title

### Problem Statement

Tak has `N` cards. On the `i`-th `(1 ≤ i ≤ 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 ≤ N ≤ 50``1 ≤ A ≤ 50``1 ≤ x`_{i}≤ 50`N,\,A,\,x`are integers._{i}

### Input

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

NAx_{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`.

### Sample Input 1

4 8 7 9 8 9

### Sample Output 1

5

- The following are the
`5`ways to select cards such that the average is`8`:- Select the
`3`-rd card. - Select the
`1`-st and`2`-nd cards. - Select the
`1`-st and`4`-th cards. - Select the
`1`-st,`2`-nd and`3`-rd cards. - Select the
`1`-st,`3`-rd and`4`-th cards.

- Select the

### Sample Input 2

3 8 6 6 9

### Sample Output 2

0

### Sample Input 3

8 5 3 6 2 8 7 6 5 9

### Sample Output 3

19

### Sample Input 4

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

### Sample Output 4

8589934591

- The answer may not fit into a
`32`-bit integer.

### Tags

### Subtasks and Limits

Subtask | Score | #TC | Time | Memory | Scoring |
---|---|---|---|---|---|

1 | 100 | 24 | 1s | 256MB | Minimum |

2 | 0 | 4 | 1s | 256MB | Minimum |

### Judge Compile Command

g++-7 ans.cpp -o cardselect -Wall -static -O2 -lm -m64 -s -w -std=gnu++17 -fmax-errors=512