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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;

import java.util.NoSuchElementException;


public class Main{
	static FastScanner sc = new FastScanner();
	static PrintWriter out = new PrintWriter(System.out);
	static int n;	
	static final int mod = 1_000_000_007;
	static long fac [];
	
	public static void main(String[] args) {
		n = sc.nextInt();
		int p = sc.nextInt();
		
		long one = 0;
		long zero = 0;
		int a = 0;
		for (int i=0; i<n; i++) {
			a = sc.nextInt();
			if (a%2==0)
				zero++;
			else
				one++;
		}
		
		long ans = 0;
		
		build_fac(50);
		
		if (p==0) {
			if (zero==0) {
				if (one==1)
					ans = 1;
				
				else {
					for (int i=2; i<=one; i+=2) {
						ans += nCr((int)one, i);
					}
				}
			}
			
			else {
				long even = pow(2L, (int)zero);
				long odd = 0;
				for (int i=2; i<=one; i+=2) {
					odd += nCr((int)one, i);
				}
				
				if (odd!=0)
					ans = even*odd;
				
				else
					ans = even;
			}
			
			if (n!=1)
				out.println(ans+1);
			
			else
				out.println(ans);
		}
		
		if (p==1) {
			if (zero==0) {
				if (one==1)
					ans = 1;
				
				else {
					for (int i=1; i<=one; i+=2) {
						ans += nCr((int)one, i);
					}
				}
			}
			
			else {
				long even = pow(2L, (int)zero);
				long odd = 0;
				
				for (int i=1; i<=one; i+=2) {
					odd += nCr((int)one, i);
				}
				
				ans = even*odd;
				
			}
			
			out.println(ans);
		}
		
		
		
		out.flush();
		
	}

	static void build_fac(int j) {
		fac = new long [j+1];
		fac[0]=1;
		
		for (int i=1; i<=j; i++) {
			fac[i] = (i*fac[i-1])%mod;
		}
	}
	
	public static long pow (long a, int j) {
	    long res=1;
	    while (j>0) {
	        if ((j-j/2*2)==1) {
	            res=(res*a)%mod;
	        }
	        a=(a*a)%mod;
	        j>>=1;
	    }
	    return res;
	}
 
	public static long modinv(long j) {
		return pow(j, mod-2);
	}
 
	public static long nCr(int j, int r) {
		return (fac[j] * modinv(fac[j-r]) % mod * modinv(fac[r]))%mod;
	}
	
	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;
	    }

	    private void skipUnprintable() {
	      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
	    }

	    public boolean hasNext() {
	      skipUnprintable();
	      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 double nextDouble () {
	    	return Double.parseDouble(next());
	    }

	    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() {
	      return (int) nextLong();
	    }

	    public int[] nextIntArray(int N, boolean oneBased) {
	      if (oneBased) {
	        int[] array = new int[N + 1];
	        for (int i = 1; i <= N; i++) {
	          array[i] = sc.nextInt();
	        }
	        return array;
	      } else {
	        int[] array = new int[N];
	        for (int i = 0; i < N; i++) {
	          array[i] = sc.nextInt();
	        }
	        return array;
	      }
	    }

	    public long[] nextLongArray(int N, boolean oneBased) {
	      if (oneBased) {
	        long[] array = new long[N + 1];
	        for (int i = 1; i <= N; i++) {
	          array[i] = sc.nextLong();
	        }
	        return array;
	      } else {
	        long[] array = new long[N];
	        for (int i = 0; i < N; i++) {
	          array[i] = sc.nextLong();
	        }
	        return array;
	      }
	    }
	  }
}