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.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
import java.util.Map.Entry;
import java.util.stream.IntStream;

public class Main {
    static ContestScanner in;
    static Writer out;
    public static void main(String[] args) {
        Main main = new Main();
        try {
            in = new ContestScanner();
            out = new Writer();
            main.solve();
            out.close();
            in.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    void solve() throws IOException {
        int n = in.nextInt();
        int p = in.nextInt();
        int odd = 0;
        int even = 0;
        for (int i = 0; i < n; i++) {
            if(in.nextInt() % 2 == 0) even++;
            else odd++;
        }
        long ans = 0;
        long[][] comb = pascalT(odd + 1);
        for (int i = 0; i <= odd; i++) {
            if(i % 2 != p) continue;
            ans += (1L << even) * comb[odd][i];
        }
        System.out.println(ans);
    }

    public static long[][] pascalT(int n){
        long[][] tri = new long[n][];
        for(int i=0; i<n; i++){
            tri[i] = new long[i+1];
            for(int j=0; j<i+1; j++){
                if(j == 0 || j == i){
                    tri[i][j] = 1;
                }else{
                    tri[i][j] = tri[i-1][j-1] + tri[i-1][j];
                }
            }
        }
        return tri;
    }
}


class Writer extends PrintWriter{
    public Writer(String filename)throws IOException
    {super(new BufferedWriter(new FileWriter(filename)));}
    public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
    private BufferedReader in;private int c=-2;
    public ContestScanner()throws IOException
    {in=new BufferedReader(new InputStreamReader(System.in));}
    public ContestScanner(String filename)throws IOException
    {in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
    public String nextToken()throws IOException {
        StringBuilder sb=new StringBuilder();
        while((c=in.read())!=-1&&Character.isWhitespace(c));
        while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public String readLine()throws IOException{
        StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
        while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public long nextLong()throws IOException,NumberFormatException
    {return Long.parseLong(nextToken());}
    public int nextInt()throws NumberFormatException,IOException
    {return(int)nextLong();}
    public double nextDouble()throws NumberFormatException,IOException
    {return Double.parseDouble(nextToken());}
    public void close() throws IOException {in.close();}
}
