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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

#pragma warning disable IDE1006
#pragma warning disable IDE0011
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using static System.Convert;
using static System.Math;
using static Extentions;

class IO
{
    int idx;
    string[] line;

    public void R(params char[] sep) { line = Console.ReadLine().Split(sep); idx = 0; }
    public string S => line[idx++];
    public string[] Ss => line.Skip(idx++).ToArray();
    public char C => char.Parse(line[idx++]);
    public char[] Cs => line.Skip(idx++).Select(char.Parse).ToArray();
    public int I => int.Parse(line[idx++]);
    public int[] Is => line.Skip(idx++).Select(int.Parse).ToArray();
    public long L => long.Parse(line[idx++]);
    public long[] Ls => line.Skip(idx++).Select(long.Parse).ToArray();
    public double F => double.Parse(line[idx++]);
    public double[] Fs => line.Skip(idx++).Select(double.Parse).ToArray();
    public decimal D => decimal.Parse(line[idx++]);
    public decimal[] Ds => line.Skip(idx++).Select(decimal.Parse).ToArray();
    public BigInteger B => BigInteger.Parse(line[idx++]);
    public BigInteger[] Bs => line.Skip(idx++).Select(BigInteger.Parse).ToArray();

    public void Write<T>(params T[] xs)
    {
        Console.Write(xs.First());
        foreach (var x in xs.Skip(1)) Console.Write(" " + x);
        Console.WriteLine();
    }
    public void Write(params object[] xs)
    {
        Console.Write(xs.First());
        foreach (var x in xs.Skip(1)) Console.Write(" " + x);
        Console.WriteLine();
    }
}

static class Extentions
{
    public static BigInteger Fact(long x)
    {
        BigInteger a = 1;
        for (var i = 2L; i <= x; i++) a *= i;
        return a;
    }

    public static long C(long n, long r)
    {
        return (long)(Fact(n) / Fact(n - r) / Fact(r));
    }
}

static class Program
{
    public static void Main()
    {
#if !DEBUG
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
#endif
        Solve(new IO());
        Console.Out.Flush();
    }

    public static void Solve(IO io)
    {
        io.R();
        var n = io.L;
        var p = io.L;
        io.R();
        var a = io.Ls;

        var even = a.LongCount(x => x % 2 == 0);
        var odd = a.LongCount(x => x % 2 == 1);

        long ans;

        if (p == 0)
        {
            ans = even + 1;
            for (var i = 2L; i <= odd; i += 2) ans += C(odd, i);
        }
        else
        {
            var tmp1 = 0L;
            for (var i = 1L; i <= odd; i += 2) tmp1 += C(odd, i);
            var tmp2 = 0L;
            for (var i = 0L; i <= even; i++) tmp2 += C(even, i);
            ans = tmp1 * tmp2;
        }

        io.Write(ans);
    }
}