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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define lowbit(i) ((i)&(-(i)))
#define lson(i) ((i)<<1)
#define rson(i) ((i)<<1|1)
#define sqr(x) ((x)*(x))
#define fi first
#define se second
#define mp(x,y) make_pair((x),(y))
#define pb push_back
using namespace std;

typedef long long ll;
typedef unsigned long long ul;
typedef pair<int,int> pii;
typedef vector<int> vii;
typedef vector<pii> vpi;
typedef queue<int> qii;

const int inf=0x3f3f3f3f;
const int maxn=2e6+5;
const long long MOD=1e9+7;

char s[maxn],t[maxn];
int fail[maxn],refail[maxn];

void getfail(int *fail,char *s){
	fail[0]=-1;
	int i=0,j=-1;
	while(s[i]){
		if(j==-1 || s[i]==s[j]){
			fail[i+1]=j+1;
			i++;
			j++;
		}
		else{
			j=fail[j];
		}
	}
}

int main(){
	scanf("%s",&s);
	ll ans=0;
	int len=strlen(s);
	for(int i=0;s[i];i++){
		t[i]=s[len-i-1];
	}
	t[len]='\0';
	getfail(fail,s);
	getfail(refail,t);
	int m;
	if(fail[len]==0 || len%(len-fail[len])){
		m=1;
	}
	else{
		m=2;
	}
	bool flag=1;
	for(int i=1;s[i];i++){
		if(s[i]!=s[i-1]){
			flag=0;
		}
	}
	if(flag){
		m=len;
	}
	if(m==1 || flag){
		ans=1;
	}
	else{
		for(int i=0;i<len-1;i++){
			int k=len-i-1;
			if((fail[i+1]==0 || (i+1)%(i+1-fail[i+1])) && (refail[k]==0 || k%(k-refail[k]))){
				ans++;
				ans%=MOD;
			}
		}
	}
	cout<<m<<endl<<ans%MOD<<endl;
	return 0;
}