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.

Examples

Input

2 0
1 3


Output

2


Input

1 1
50


Output

0


Input

3 0
1 1 1


Output

4


Input

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


Output

17592186044416
import java.util.*;
public class Main {
        static Scanner sc = new Scanner(System.in);
        static void myout(Object t){System.out.println(t);}//standard output
        static void myerr(Object t){System.err.println(t);}//standard error
        static String getStr(){return sc.next();}
        static int getInt(){return Integer.parseInt(getStr());}
        static long getLong(){return Long.parseLong(getStr());}
        static boolean isNext(){return sc.hasNext();}
        static String[] mySplit(String str){return str.split("");}
        public static void main(String[] args){
          long N = getLong();
          int P = getInt();
            boolean isOdd = false;
            for(int i = 0; i < N; i++){
              int a = getInt();
              if(a % 2 == 1){
                isOdd = true;
              }
            }
            if(isOdd){
              myout(originPow(new Long(2),N - 1));
            }else{
              if(P == 0){
                myout(originPow(new Long(2),N));
              }else{
                myout(0);
              }
            }
          
        }
        //Method addition frame start
static long originPow(long x, long n) {return originPow(x,n,-1);}
static long originPow(long x, long n,int m) {
        long ans = 1;
        while (n > 0) {
                if ((n & 1) == 1){
                  ans = ans * x;
                  if(m != -1){ans %= m;}
                }
                x = x * x;
          		if(m != -1){x %= m;}
                n >>= 1;
        }
        return ans;
}
        //Method addition frame end
}
