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: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }

        static void Main(string[] args)
        {
            //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
            var NP = Sarray();
            var N = NP[0];
            var P = NP[1];
            var Ai = Sarray();
            var eNum = Ai.Count(a => a % 2 == 0);
            var oNum = Ai.Count() - eNum;
            var cmb = new Combination(51);

            //偶数を1つ以上使い、奇数を使わない場合
            var allE = 0L; ;
            for (var i = 1; i <= eNum; ++i)
            {
                allE += (long)cmb.com(eNum, i);
            }
            //偶数
            if (P == 0)
            {
                //奇数を1つ以上使い、偶数を使わない場合
                var allO = 0L;
                for (var i = 2; i <= oNum; i += 2)
                {
                    allO += (long)cmb.com(oNum, i);
                }
                //何も使わない、偶数のみ使う、奇数のみ、偶数と奇数を使うの足し合わせ
                WriteLine(1 + allE + allO + allE * allO);
                return;
            }
            //奇数を1つ以上使い、偶数を使わない場合
            var allOd = 0L;
            for (var i = 1; i <= oNum; i += 2)
            {
                allOd += (long)cmb.com(oNum, i);
            }
            //奇数のみ、偶数と奇数を使う場合の多幸せ
            WriteLine(allOd + allE * allOd);
            //Out.Flush();
        }
        public class Combination
        {
            double[,] dp;
            public Combination(long n)
            {
                dp = new double[n + 1, n + 1];
                for (var i = 0; i < n + 1; ++i)
                {
                    dp[i, 0] = 1;
                    dp[i, i] = 1;
                }
                for (var i = 2; i < n + 1; ++i)
                    for (var j = 1; j < i; ++j)
                        dp[i, j] = dp[i - 1, j - 1] + dp[i - 1, j];
            }
            public double com(int n, int k)
            {
                if (n < k) return 0;
                if (n < 0 | k < 0) return 0;
                return dp[n, k];
            }
        }
    }
}