Problem:
Score : 200 points

Problem Statement

There are N bags of biscuits. The i-th bag contains A_i biscuits.

Takaki will select some of these bags and eat all of the biscuits inside.
Here, it is also possible to select all or none of the bags.

He would like to select bags so that the total number of biscuits inside is congruent to P modulo 2.
How many such ways to select bags there are?

Constraints

1 \leq N \leq 50

P = 0 or 1

1 \leq A_i \leq 100

Input

Input is given from Standard Input in the following format:

N P
A_1 A_2 ... A_N

Output

Print the number of ways to select bags so that the total number of biscuits inside is congruent to P modulo 2.

Sample Input 1

2 0
1 3

Sample Output 1

2

There are two ways to select bags so that the total number of biscuits inside is congruent to 0 modulo 2:

Select neither bag. The total number of biscuits is 0.

Select both bags. The total number of biscuits is 4.

Sample Input 2

1 1
50

Sample Output 2

0

Sample Input 3

3 0
1 1 1

Sample Output 3

4

Two bags are distinguished even if they contain the same number of biscuits.

Sample Input 4

45 1
17 55 85 55 74 20 90 67 40 70 39 89 91 50 16 24 14 43 24 66 25 9 89 71 41 16 53 13 61 15 85 72 62 67 42 26 36 66 4 87 59 91 4 25 26

Sample Output 4

17592186044416

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define ll long long
using namespace std;
ll C[55][55];
// Prototype of a utility function that returns minimum of two integers
ll min(ll a, ll b);
 
// Returns value of Binomial Coefficient C(n, k)
ll binomialCoeff(ll n, ll k)
{
    
    ll i, j;
 
    // Caculate value of Binomial Coefficient in bottom up manner
    for (i = 0; i <= n; i++)
    {
        for (j = 0; j <= min(i, k); j++)
        {
            // Base Cases
            if (j == 0 || j == i)
                C[i][j] = 1;
 
            // Calculate value using previosly stored values
            else
                C[i][j] = C[i-1][j-1] + C[i-1][j];
        }
    }
 
    return C[n][k];
}
 
// A utility function to return minimum of two llegers
ll min(ll a, ll b)
{
    return (a<b)? a: b;
}
 
/* Drier program to test above function*/
int main()
{
	ll n,k,odd=0,even=0;
	cin>>n>>k;
	ll a[n];
	for(ll i=0;i<n;i++)
	{
		cin>>a[i];
		if(a[i]&1)
		odd++;
		else
		even++;
	}
	binomialCoeff(n,n);
	if(k&1)
	{
		ll ans=0,first=0,second=0;
//		cout<<"hello "<<odd<<" "<<even<<endl;
		for(int i=0;i<=even and even!=0;i++)
		{
			first+=C[even][i];
		}
		for(int i=1;i<=odd and odd!=0;i+=2)
		{
			second+=C[odd][i];			
		}
	//	cout<<first<<" "<<second<<endl;
		if(first==0)
		cout<<second;
		else if(second==0)
		cout<<"0";
		else
		cout<<first*second;
	}
	else
	{
		ll ans=0,first=0,second=0;
		for(int i=0;i<=even and even!=0;i++)
		{
			first+=C[even][i];
		}
		for(int i=0;i<=odd and odd!=0;i+=2)
		{
			second+=C[odd][i];			
		}
		if(first==0)
		cout<<second;
		else if(second==0)
		cout<<first;
		else
		cout<<first*second<<endl;
	}
    return 0;
}