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.io.*;
import java.util.*;
public class Main {
    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int n = fs.nextInt();
        int odd = 0;
        int even = 0;
        int p = fs.nextInt();
        for(int i=0;i<n;i++){
            if(fs.nextInt()%2==0){
                even++;
            }else{
                odd++;
            }
        }
        long sum = 1;
        if(p==0){
            for(int i=0;i<odd-1;i++){
                sum*=2;
            }
        }else{
            if(odd==0){
                System.out.println(0);
                return;
            }
            for(int i=0;i<odd-1;i++){
                sum*=2;
            }
        }
        for(int i=0;i<even;i++){
            sum*=2;
        }
        System.out.println(sum);

    }
    static class FastScanner {
            private final InputStream in = System.in;
            private final byte[] buffer = new byte[1024];
            private int ptr = 0;
            private int buflen = 0;
            private boolean hasNextByte() {
                if (ptr < buflen) {
                    return true;
                }else{
                    ptr = 0;
                    try {
                        buflen = in.read(buffer);
                    } catch (IOException e) {
                        e.printStackTrace();
                    }
                    if (buflen <= 0) {
                        return false;
                    }
                }
                return true;
            }
            private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
            private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
            public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
            public String next() {
                if (!hasNext()) throw new NoSuchElementException();
                StringBuilder sb = new StringBuilder();
                int b = readByte();
                while(isPrintableChar(b)) {
                    sb.appendCodePoint(b);
                    b = readByte();
                }
                return sb.toString();
            }
            public long nextLong() {
                if (!hasNext()) throw new NoSuchElementException();
                long n = 0;
                boolean minus = false;
                int b = readByte();
                if (b == '-') {
                    minus = true;
                    b = readByte();
                }
                if (b < '0' || '9' < b) {
                    throw new NumberFormatException();
                }
                while(true){
                    if ('0' <= b && b <= '9') {
                        n *= 10;
                        n += b - '0';
                    }else if(b == -1 || !isPrintableChar(b)){
                        return minus ? -n : n;
                    }else{
                        throw new NumberFormatException();
                    }
                    b = readByte();
                }
            }
            public int nextInt() {
                long nl = nextLong();
                if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
                return (int) nl;
            }
            public double nextDouble() { return Double.parseDouble(next());}
        }
}
