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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
	"strings"
)

type bufReader struct {
	r   *bufio.Reader
	buf []byte
	i   int
}

var reader = &bufReader{
	bufio.NewReader(os.Stdin),
	make([]byte, 0),
	0,
}

func (r *bufReader) readLine() {
	if r.i < len(r.buf) {
		return
	}
	r.buf = make([]byte, 0)
	r.i = 0
	for {
		line, isPrefix, err := r.r.ReadLine()
		if err != nil {
			panic(err)
		}
		r.buf = append(r.buf, line...)
		if !isPrefix {
			break
		}
	}
}

func (r *bufReader) next() string {
	r.readLine()
	from := r.i
	for ; r.i < len(r.buf); r.i++ {
		if r.buf[r.i] == ' ' {
			break
		}
	}
	s := string(r.buf[from:r.i])
	r.i++
	return s
}

func (r *bufReader) nextLine() string {
	r.readLine()
	s := string(r.buf[r.i:])
	r.i = len(r.buf)
	return s
}

var writer = bufio.NewWriter(os.Stdout)

func next() string {
	return reader.next()
}

func nextInt64() int64 {
	i, err := strconv.ParseInt(reader.next(), 10, 64)
	if err != nil {
		panic(err)
	}
	return i
}

func nextInt() int {
	return int(nextInt64())
}

func nextLine() string {
	return reader.nextLine()
}

func out(a ...interface{}) {
	fmt.Fprintln(writer, a...)
}

func max64(x, y int64) int64 {
	if x > y {
		return x
	}
	return y
}

func max(x, y int) int {
	return int(max64(int64(x), int64(y)))
}

func min64(x, y int64) int64 {
	if x < y {
		return x
	}
	return y
}

func min(x, y int) int {
	return int(min64(int64(x), int64(y)))
}

func abs64(x int64) int64 {
	if x < 0 {
		return -x
	}
	return x
}

func abs(x int) int {
	return int(abs64(int64(x)))
}

func joinInt64s(a []int64, sep string) string {
	b := make([]string, len(a))
	for i, v := range a {
		b[i] = strconv.FormatInt(v, 10)
	}
	return strings.Join(b, sep)
}

func joinInts(a []int, sep string) string {
	b := make([]string, len(a))
	for i, v := range a {
		b[i] = strconv.Itoa(v)
	}
	return strings.Join(b, sep)
}

func divUp64(x, y int64) int64 {
	return (x + y - 1) / y
}

func divUp(x, y int) int {
	return int(divUp64(int64(x), int64(y)))
}

func gcd64(x, y int64) int64 {
	if x < y {
		x, y = y, x
	}
	for y != 0 {
		x, y = y, x%y
	}
	return x
}

func gcd(x, y int) int {
	return int(gcd64(int64(x), int64(y)))
}

func lcm64(x, y int64) int64 {
	return x * y / gcd64(x, y)
}

func lcm(x, y int) int {
	return int(lcm64(int64(x), int64(y)))
}

func pow64(x, y int64) int64 {
	return int64(math.Pow(float64(x), float64(y)))
}

func pow(x, y int) int {
	return int(pow64(int64(x), int64(y)))
}

func main() {
	solve()
	writer.Flush()
}

func solve() {
	N, A := nextInt(), nextInt()
	x := make([]int, N)
	for i := 0; i < N; i++ {
		x[i] = nextInt()
	}
	dp := make([][][]int, N+1)
	for i := 0; i <= N; i++ {
		dp[i] = make([][]int, N+1)
		for j := 0; j <= N; j++ {
			dp[i][j] = make([]int, N*A+1)
		}
	}
	for i := 0; i <= N; i++ {
		for j := 0; j <= N; j++ {
			for k := 0; k <= N*A; k++ {
				if i == 0 && j == 0 && k == 0 {
					dp[i][j][k] = 1
					continue
				}
				if i > 0 && k < x[i-1] {
					dp[i][j][k] = dp[i-1][j][k]
					continue
				}
				if i > 0 && j >= 1 && k >= x[i-1] {
					dp[i][j][k] = dp[i-1][j][k] + dp[i-1][j-1][k-x[i-1]]
					continue
				}
				dp[i][j][k] = 0
			}
		}
	}
	ans := 0
	for i := 1; i <= N; i++ {
		ans += dp[N][i][i*A]
	}
	out(ans)
}