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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;

namespace kyoupuro {

    class MainClass {

        public static void Main() {
            var N = Input.NextInt();
            var A = Input.NextInt();
            var list = Input.IntList();
            var dp = new long[N + 1, N + 1, 5000]; // inputの順番, 枚数, 合計

            dp[0, 0, 0] = 1;

            for (int i = 0; i < N; i++) {
                for (int j = 0; j < N; j++) {
                    for (int sum = 0; sum < 4000; sum++) {
                        dp[i + 1, j, sum] += dp[i, j, sum];
                        dp[i + 1, j + 1, sum + list[i]] += dp[i, j, sum];
                    }
                }
            }

            long count = 0;
            for (int i = 1; i <= N; i++) {
                count += dp[N, i, i * A];
            }
            Console.WriteLine(count);
        }
    }

    class Input {
        static IEnumerator<string> enumerator;

        public static string Line() {
            return Console.ReadLine();
        }

        public static int NextInt() {
            if (enumerator == null || !enumerator.MoveNext()) {
                enumerator = StrArr().AsEnumerable().GetEnumerator();
                enumerator.MoveNext();
            }
            return int.Parse(enumerator.Current);
        }

        public static long NextLong() {
            if (enumerator == null || !enumerator.MoveNext()) {
                enumerator = StrArr().AsEnumerable().GetEnumerator();
                enumerator.MoveNext();
            }
            return long.Parse(enumerator.Current);
        }

        public static string[] StrArr() {
            return Line().Split(' ');
        }

        public static List<int> IntList() {
            return StrArr().Select(int.Parse).ToList();
        }

        public static List<long> LongList() {
            return StrArr().Select(long.Parse).ToList();
        }

        public static void Skip(int line = 1) {
            enumerator.Reset();
            for (int i = 0; i < line; i++) Console.ReadLine();
        }

        public static void Reset() {
            enumerator.Reset();
        }
    }
}