Problem:
Score : 300 points

Problem Statement

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.

Partial Score

200 points will be awarded for passing the test set satisfying 1 \leq N \leq 16.

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.

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.

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.

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
class Solve{
    public long n;
    public long s;
    public Solve(){}
    public static int Main(){
        new Solve().Calc();
        return 0;
    }
    void Calc(){
        getinput();
        if(n <= s){
            if(n == s){
                Console.WriteLine(n+1);
            }
            else{
                Console.WriteLine(-1);
            }
        }
        else{
            long i;
            for(i=2;i*i<=n;i++){
                long sum = 0;
                long a = n;
                while(a > 0){
                    sum += a%i;
                    a /= i;
                }
                if(sum == s){
                    Console.WriteLine(i);
                    return;
                }
            }
            if(i > s)
                i = s;
            for(;i>=1;i--){
                if((n-s+i)%i == 0 && (n-s+i)/i > i && s-i < (n-s+i)/i){
                    Console.WriteLine((n-s+i)/i);
                    return;
                }
            }
            Console.WriteLine(-1);
        }
    }
    void getinput(){
        n = int.Parse(Console.ReadLine());
        s = int.Parse(Console.ReadLine());
    }    
}