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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
#if !DEBUG
    using System.IO;
#endif

public class Program {
    public static void Main() {
        #region SetAutoFlushIsFalse
#if !DEBUG
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        Console.SetOut(sw);
#endif
        #endregion
        var arr = ReadLib.ReadAsIntArray();
        var n = arr[0];
        var p = arr[1];
        var aArr = ReadLib.ReadAsIntArray().Select(i => i % 2 == 0 ? true : false);
        var nEven = aArr.Count(i => i == true);
        var nOdd = aArr.Count(i => i == false);
        long nOddCombination, nEvenCombination;

        if (p == 1) {
            nOddCombination = Enumerable.Range(0, nOdd).Where(i => i % 2 == 1).Select(c => MyMath.Combination(n, c)).Sum();
            nEvenCombination = Enumerable.Range(0, nEven).Where(i => i % 2 == 0).Select(c => MyMath.Combination(n, c)).Sum();
        } else {
            nOddCombination = Enumerable.Range(0, nOdd).Where(i => i % 2 == 0).Select(c => MyMath.Combination(n, c)).Sum();
            nEvenCombination = Enumerable.Range(0, nEven).Where(i => i % 2 == 1).Select(c => MyMath.Combination(n, c)).Sum();
        }

        Console.WriteLine(nOddCombination * nEvenCombination);
        #region Flush
#if !DEBUG
        Console.Out.Flush();
        sw.Close();
#endif
        #endregion
    }

    static long[] Create(int item, long[] patterns) {
        var ret = new List<long>();
        foreach (var pattern in patterns) {
            ret.Add(pattern);
            ret.Add(pattern + item);
        }
        return ret.ToArray();
    }
}

static class ReadLib {
    public static long ReadAsLong() {
        return long.Parse(Console.ReadLine());
    }

    public static int ReadAsInt() {
        return int.Parse(Console.ReadLine());
    }

    public static int[] ReadAsIntArray() {
        return Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
    }

    public static long[] ReadAsLongArray() {
        return Console.ReadLine().Split(' ').Select(s => long.Parse(s)).ToArray();
    }

    public static ulong[] ReadAsULongArray() {
        return Console.ReadLine().Split(' ').Select(s => ulong.Parse(s)).ToArray();
    }

    public static string[] ReadAsStringArray() {
        return Console.ReadLine().Split(' ');
    }

    public static int[] ReadNTimesAsInt(int n) {
        return Enumerable.Range(1, n).Select(s => int.Parse(Console.ReadLine())).ToArray();
    }

    public static int[][] ReadNTimesAsIntArray(int n) {
        return Enumerable.Range(1, n).Select(s => ReadAsIntArray()).ToArray();
    }

}

static class MyMath {
    /// <summary>階乗</summary>
    public static long Factorial(long n) {
        if (n == 0) {
            return 1;
        }
        return n * Factorial(n - 1);
    }

    /// <summary>nCk, 組み合わせ</summary>
    public static long Combination(long n, long k) {
        return Factorial(n) / Factorial(k) * Factorial(n - k);
    }
}