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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            Scanner cin = new Scanner();
            int N = cin.Int();
            int P = cin.Int();
            int[] A = cin.ArrayInt(N);

            bool flag = true; //偶数のみ
            for (int i = 0; i < N; i++)
            {
                if (A[i] % 2 != 0) flag = false;
            }

            Console.WriteLine(flag ? P == 0 ? (long)Math.Pow(2, N) : 0 : Math.Pow(2, N - 1));
            Console.ReadLine();
        }

        static string GetNextPermutation(string pTarget)
        {
            var query = pTarget.ToCharArray().OrderBy(X => X);
            string BaseStr = "";
            foreach (char each in query)
            {
                BaseStr += each;
            }

            var stk = new Stack<string>();

            for (int I = 0; I <= BaseStr.Length - 1; I++)
            {
                stk.Push(BaseStr[I].ToString());
            }

            var answerList = new List<string>();

            while (stk.Count > 0)
            {
                string wkStr = stk.Pop();

                if (wkStr.Length == BaseStr.Length)
                {
                    answerList.Add(wkStr);
                    continue;
                }

                for (int I = 0; I <= BaseStr.Length - 1; I++)
                {
                    if (wkStr.Contains(BaseStr[I].ToString()) == false)
                    {
                        stk.Push(wkStr + BaseStr[I].ToString());
                    }
                }
            }

            foreach (string each in answerList.OrderBy(X => X))
            {
                if (pTarget.CompareTo(each) >= 0) continue;
                return each;
            }
            return pTarget;
        }

        static long Factorial(int n) //階乗
        {
            if (n == 1) return 1;
            return n * Factorial(n - 1);
        }

        static long Permutaion(int n, int k) //順列
        {
            long ans = 1;
            for (int i = 0; i < k; i++)
            {
                ans *= (n - i);
            }
            return ans;
        }

        static long Combination(int n, int k) //組み合わせ
        {
            long ans = 1;
            for (int i = n; i > n - k; --i)
            {
                ans = ans * i;
            }
            for (int i = 1; i < k + 1; ++i)
            {
                ans = ans / i;
            }
            return ans;
        }

        static int GCD(int a, int b) //a,bの最大公約数
        {
            if (a < b)
                // 引数を入替えて自分を呼び出す
                return GCD(b, a);
            while (b != 0)
            {
                var remainder = a % b;
                a = b;
                b = remainder;
            }
            return a;
        }

        static int LCM(int a, int b) //a,bの最小公倍数
        {
            return a / GCD(a, b) * b;
        }
    

        static int BinarySearch<T>(T[] array, T target) where T : IComparable<T> //2分探索
        {
            int min = 0;
            int max = array.Length - 1;

            while (true)
            {
                // 範囲内に見つからなかった
                if (max < min) return -1;
                // 範囲内の中央値と比較する
                int mid = min + (max - min) / 2;
                switch (target.CompareTo(array[mid]))
                {
                    case -1:    // 中央値より小さい
                        max = mid - 1;
                        break;
                    case 1:     // 中央値より大きい
                        min = mid + 1;
                        break;
                    case 0:     // 見つかった
                        return mid;
                }
            }
        }

        static void Swap<T>(ref T a, ref T b) //入れ替え
        {
            T tmp = a;
            a = b;
            b = tmp;
        }
    }

    class Scanner //標準入力
    {
        string[] s;
        int i;

        char[] cs = new char[] { ' ' };

        public Scanner()
        {
            s = new string[0];
            i = 0;
        }

        public string next()
        {
            if (i < s.Length) return s[i++];
            string st = Console.ReadLine();
            while (st == "") st = Console.ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            if (s.Length == 0) return next();
            i = 0;
            return s[i++];
        }

        public int Int()
        {
            return int.Parse(next());
        }
        public int[] ArrayInt(int N, int add = 0)
        {
            int[] Array = new int[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = Int() + add;
            }
            return Array;
        }

        public long Long()
        {
            return long.Parse(next());
        }

        public long[] ArrayLong(int N, long add = 0)
        {
            long[] Array = new long[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = Long() + add;
            }
            return Array;
        }

        public double Double()
        {
            return double.Parse(next());
        }


        public double[] ArrayDouble(int N, double add = 0)
        {
            double[] Array = new double[N];
            for (int i = 0; i < N; i++)
            {
                Array[i] = Double() + add;
            }
            return Array;
        }
    }
}

/* Dictionaryのvalueが特定の値をとっている要素を削除する
var removeTargetLst = dic.Where(kv => kv.Value == value).ToList();
foreach(var item in removeTargetLst)
{
   dic.Remove(item.Key);
}
*/