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;

using System.Runtime.CompilerServices;
using ll=System.Int64;

public class Contest
{
	static void Swap1<T>(ref T a, ref T b) { T t = a; a = b; b = t; }
	static void Swap2<T>(ref T a, ref T b) where T : IComparable { if (a.CompareTo(b)==1) Swap1(ref a, ref b); }  // b の方が小さければ交換
	static bool Chmin<T>(ref T a, T b) where T : IComparable { if (a.CompareTo(b)== 1) { a = b; return true; } return false; }  // b の方が小さければ a を更新
	static bool Chmax<T>(ref T a, T b) where T : IComparable { if (a.CompareTo(b)==-1) { a = b; return true; } return false; }  // b の方が大きければ a を更新
	static T[][] InitMat<T>(long len1, long len2, T val){ T[][] m = new T[len1][]; for (int i = 0; i < m.Length; i++) m[i] = Enumerable.Repeat(val, (int)len2).ToArray(); return m; }
	static T[][][] InitMat<T>(long len1, long len2, long len3, T val){ T[][][] m = new T[len1][][]; for (int i = 0; i < m.Length; i++) m[i] = InitMat(len2,len3,val); return m; }
	public const long MOD1 = 1000000007; // 10^9+7
	public const double EPS1 = 1e-8;

	public static void Main() {
		Solve_A();
 	}

	public static void Solve_A() {
		long  n, a;
		MyIO.ReadMulti(out n, out a);
		ll[] x;
		MyIO.ReadArray(out x);

		ll[][][] dp = InitMat(n+1,n+1,50*n+1, 0L);
		dp[0][1][x[0]] = 1;
		dp[0][0][0] = 1;
		for (int i = 1; i < n; i++)
		{
			for (int j = 0; j <= (i+1); j++)
			{
				for (int k = 0; k <= 50*(i+1); k++)
				{
					ll v = dp[i-1][j][k];
					v += (0<j&&x[i]<=k)?dp[i-1][j-1][k-x[i]]:0;
					dp[i][j][k] = v;
				}
			}
		}

		long ans = 0;
		for (int j = 1; j <= n; j++)
		{
			for (int k = 0; k <= 50*n; k++)
			{
				if(k%j==0&&k/j==a) ans += dp[n-1][j][k];
			}
		}

		MyIO.WriteMulti(ans);
	}
	public static void Solve_B() {
		long  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;


		MyIO.WriteMulti(ans);
	}
	public static void Solve_C() {
		long  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;


		MyIO.WriteMulti(ans);
	}
	public static void Solve_D() {
		long  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;


		MyIO.WriteMulti(ans);
	}
	public static void Solve_E() {
		long  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;


		MyIO.WriteMulti(ans);
	}
	public static void Solve_F() {
		long  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;


		MyIO.WriteMulti(ans);
	}










}




















#region MyIO

public struct VT<T, U>
{
	public T Item1; public U Item2;
    public VT(T a, U b) { Item1 = a; Item2 = b; }
}
public struct VT<T, U, V>
{
	public T Item1; public U Item2; public V Item3;
    public VT(T a, U b, V c) { Item1 = a; Item2 = b; Item3 = c; }
}
public struct VT<T, U, V, W>
{
	public T Item1; public U Item2; public V Item3; public W Item4;
    public VT(T a, U b, V c, W d) { Item1 = a; Item2 = b; Item3 = c; Item4 = d; }
}

public class Printer : System.IO.StreamWriter
{
	public override IFormatProvider FormatProvider { get { return System.Globalization.CultureInfo.InvariantCulture; } }
	public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
	public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { }
}
public static class MyIO
{
	private static char[] splitter = new char[] {' '};
	private static bool eq<T, U>() => typeof(T).Equals(typeof(U));
	private static T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
	private static T cv<T>(string s) =>
		eq<T, int>()    ? ct<T, int>(int.Parse(s))
	  : eq<T, long>()   ? ct<T, long>(long.Parse(s))
	  : eq<T, double>() ? ct<T, double>(double.Parse(s, System.Globalization.CultureInfo.InvariantCulture))
	  : eq<T, char>()   ? ct<T, char>(s[0])
						: ct<T, string>(s);
			
	public static string[] ReadMulti<T>(out T a) {
		var ar = Console.ReadLine().Split(splitter, StringSplitOptions.RemoveEmptyEntries); 
		a = cv<T>(ar[0]);
		return ar;
	}
	public static string[] ReadMulti<T, U>(out T a, out U b) {
		var ar = ReadMulti<T>(out a); 
        b = cv<U>(ar[1]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V>(out T a, out U b, out V c) {
		var ar = ReadMulti<T, U>(out a, out b); 
        c = cv<V>(ar[2]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W>(out T a, out U b, out V c, out W d) {
		var ar = ReadMulti<T, U, V>(out a, out b, out c); 
        d = cv<W>(ar[3]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e) {
		var ar = ReadMulti<T, U, V, W>(out a, out b, out c, out d); 
        e = cv<X>(ar[4]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f) {
		var ar = ReadMulti<T, U, V, W, X>(out a, out b, out c, out d, out e); 
        f = cv<Y>(ar[5]);
		return ar;
	}
	public static string[] ReadArray<T>(out T[] a) {		
		var ar = Console.ReadLine().Split(splitter, StringSplitOptions.RemoveEmptyEntries);
		a = ar.Select(cv<T>).ToArray();
		return ar;
	}		
	public static string[][] ReadLines<T>(long n, out T[] a) {
		a = new T[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) arr[i] = ReadMulti(out a[i]);
		return arr;
	}
	public static string[][] ReadLines<T, U>(long n, out VT<T, U>[] a) {
		a = new VT<T, U>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p;
			arr[i] = ReadMulti(out o, out p);
			a[i] = new VT<T, U>(o, p);
		}
		return arr;
	}
	public static string[][] ReadLines<T, U, V>(long n, out VT<T, U, V>[] a) {
		a = new VT<T, U, V>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p; V q;
			arr[i] = ReadMulti(out o, out p, out q);
			a[i] = new VT<T, U, V>(o, p, q);
		}
		return arr;
	}
	public static string[][] ReadLines<T, U, V, W>(long n, out VT<T, U, V, W>[] a) {
		a = new VT<T, U, V, W>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p; V q; W r;
			arr[i] = ReadMulti(out o, out p, out q, out r);
			a[i] = new VT<T, U, V, W>(o, p, q, r);
		}
		return arr;
	}
	public static string[][] ReadMatrix<T>(long n, out T[][] a) {
		a = new T[n][];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) arr[i] = ReadArray(out a[i]);
		return arr;
	}

	private static void wwp(Action act){
		var sw = new Printer(Console.OpenStandardOutput()){AutoFlush = false};
		Console.SetOut(sw);
		act();
		Console.Out.Flush();
		sw.AutoFlush = true;
		Console.SetOut(sw);
	}
	private static string wfm(Type t) =>t.Equals(typeof(double)) ? "{0:F10}" : "{0}";
	public static void WriteMulti(params object[] a) {
		wwp(()=>{
			for(int i=0;i<a.Length;i++) {
				string fs = wfm(a[i].GetType()) + ((i<a.Length-1) ? " " : Environment.NewLine);
				Console.Write(fs, a[i]);
			}
		});
	}
	public static void WriteArray<T>(T[] a) {
		wwp(()=>{
			string fs = wfm(typeof(T));
			string fs1 = fs + " ";
			string fs2 = fs + Environment.NewLine;
			for(int i=0;i<a.Length;i++) Console.Write( ((i<a.Length-1) ? fs1 : fs2), a[i]);
		});
	}
	public static void WriteLines<T>(T[] a) {
		wwp(()=>{
			string fs = wfm(typeof(T)) + Environment.NewLine;
			foreach(T x in a) Console.Write(fs, x);
		});
	}


}

#endregion