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)

  ///====================== khela STARTS HERE =====================///
#include "bits/stdc++.h"
const int inf = 1000000005;
const long long INF = 3e18;
const double pi = 2 * acos ( 0.0 );
typedef long long ll;
#define pii pair<int, int>
#define pb push_back
#define pf push_front
#define all(v) v.begin(), v.end()
#define maximum *max_element
#define minimum *min_element
#define MEMSET(v, x) memset(v, x, sizeof(v))
#define ABS(x) ((x)<0?-(x):(x))
#define white 1
#define grey 2
#define black 3
#define bug cout << "ei porjonto thikase" << endl;
#define fastread ios_base::sync_with_stdio(false);cin.tie(0);
using namespace std;
int gcd (int a, int b ) {
    a =  abs( a ); b = abs( b );
    while ( b ) { a = a % b; swap ( a, b ); } return a;}
int modInverse(int a, int m)
{int m0 = m;int y = 0, x = 1;if (m == 1)return 0;
while (a > 1){int q = a / m;int t = m;m = a % m, a = t;t = y;y = x - q * y;x = t;}if (x < 0)x += m0;return x;}
int lcm(int a, int b)
{int temp = gcd(a, b);return temp ? (a / temp * b) : 0;}
///====================== khela end1s HERE =====================///
const int maxn = 55;
int arr[maxn];
ll dp[maxn][101*101], p, n;
ll call(int i, int ammount){
	if(i>=n){
		if(ammount%2 == p)return 1;
		else{
			return 0;
		}
	}
	if(dp[i][ammount] == -1){
		ll ret1 = 0, ret2 = 0;
		ret1 = call(i+1, arr[i]+ammount);
		ret2 = call(i+1, ammount);
		dp[i][ammount] = ret1 + ret2;
	}
	return dp[i][ammount];
}

int main(int argc, char const *argv[])
{
	cin >> n >> p;
	for(int i=0; i<n; i++)cin >> arr[i];
	MEMSET(dp, -1);
	cout << call(0, 0) << endl;
}