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 (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>

#define ll long long

void swap (int *x, int *y) {
  int temp;

  temp = *x;
  *x = *y;
  *y = temp;

  return;
}


//naosu
long int gcd(long int a,long int b){
  long int c;

  while (b > 0){
    c = a % b;
    a = b;
    b = c;
  }

  return a;
}

int upll(const void*a, const void*b){
  return*(ll*)a<*(ll*)b?-1:*(ll*)a>*(ll*)b?1:0;
}

int downll(const void*a, const void*b){
  return*(ll*)a<*(ll*)b?1:*(ll*)a>*(ll*)b?-1:0;
}

void sortup(ll*a,int n){
  qsort(a,n,sizeof(ll),upll);
}

void sortdown(ll*a,int n){
  qsort(a,n,sizeof(ll),downll);
}

long int modpow(long int a,long int n,long int mod){
  long int ans=1;
  while(n>0){
    if(n & 1){
      ans=ans*a%mod;
    }
    a=a*a%mod;
    n/=2;
  }
  return ans;
}

long int modinv(long int a,long int mod){
  return modpow(a,mod-2,mod);
}

int max(int a,int b){
  if(a<b){
    return b;
  }
  else{
    return a;
  }
}

int min(int a,int b){
  if(a<b){
    return a;
  }
  else{
    return b;
  }
}

void chmax(int *a,int b){
  if(*a < b){
    *a = b;
  }

  return;
}

void chmin(int *a,int b){
  if(*a > b){
    *a =b;
  }

  return;
}


long int lcm(long int a,long int b){
  return a/gcd(a,b)*b;
}


long int f(long int n,long int c,long int d){
  long int cnt=n/c+n/d-n/lcm(c,d);
  return n-cnt;
}


/****************************************\
| Thank you for viewing my code:)        |
| Written by RedSpica a.k.a. RanseMirage |
| Twitter:@asakaakasaka                  | 
\****************************************/

int main(void){
  int MOD=1e9+7; 
  /*
  long int kai[2000000];
  long int rekai[2000000];
  
  kai[0]=1;
  kai[1]=1;
  rekai[0]=1;
  rekai[1]=1;
  for(int i=2;i<2000000;i++){
    kai[i]=kai[i-1]*i;
    kai[i]%=MOD;

    rekai[i]=rekai[i-1]*modinv(i,MOD);
    rekai[i]%=MOD;
  }
  */

  long int n,p;
  scanf("%ld%ld",&n,&p);

  long int e=0;
  long int o=0;
  for(int i=0;i<n;i++){
    int a;
    scanf("%d",&a);

    if(a%2==0){
      e++;
    }
    else{
      o++;
    }
  }

  long int ans=1;
  while(e--){
    ans*=2;
  }

  //
  long int all=0;
  if(p==0){
    //oCiのiの部分を全探索
    for(long int i=0;i<=o;i+=2){
      long int res=1;
      for(long int j=o;j>o-i;j--){
        res*=j;
        res/=(o-j+1);
      }
      all+=res;
    }
  }
  else{
    for(long int i=1;i<=o;i+=2){
      long int res=1;
      for(long int j=o;j>o-i;j--){
        res*=j;
        res/=(o-j+1);
      }
      all+=res;
    }
  }

  printf("%ld\n",all*ans);

  return 0;
}