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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
using System.Collections;
using static System.Math;
using System.Linq;
using static System.Array;

namespace ConsoleApp2
{
    class Program
    {

        static void Main(string[] args)
        {
            //var N = long.Parse(Console.ReadLine());
            var NP = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
            var N = NP[0];
            var P = NP[1];
            var A = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();

            var odd = 0;
            var eve = 0;

            for (int i = 0; i < N; i++)
            {
                if(A[i]%2 == 0)
                {
                    eve++;
                }
                else
                {
                    odd++;
                }
            }

            var ans = (long)Pow(2, eve);
            var oddall = (long)Pow(2, odd);
            var oddeve = 0;
            //oddを偶数個選ぶ場合の数
            for (int i = 0; i <= odd; i += 2)
            {
                oddeve += (int)Modular.Ncr(odd, i);
            }

            if (P == 1)
            {
                Console.WriteLine(ans*(oddall-oddeve));
            }
            else
            {
                Console.WriteLine(ans * (oddeve));
            }

            
            
        }


    }

    class Modular
    {
        private const int M = 1000000007;
        public long value;
        public Modular(long value) { this.value = value; }
        public static implicit operator Modular(long a)
        {
            var m = a % M;
            return new Modular((m < 0) ? m + M : m);
        }
        public static Modular operator +(Modular a, Modular b)
        {
            return (a.value + b.value) % M;
        }
        public static Modular operator -(Modular a, Modular b)
        {
            return a.value - b.value;
        }
        public static Modular operator *(Modular a, Modular b)
        {
            return a.value * b.value;
        }
        public static Modular Pow(Modular a, int n)
        {
            switch (n)
            {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    var p = Pow(a, n / 2);
                    return p * p * Pow(a, n % 2);
            }
        }
        public static Modular operator /(Modular a, Modular b)
        {
            return a * Pow(b, M - 2);
        }
        private static readonly List<int> facs = new List<int> { 1 };
        private static Modular Fac(int n)
        {
            for (int i = facs.Count; i <= n; ++i)
            {
                facs.Add((int)(Math.BigMul(facs.Last(), i) % M));
            }
            return facs[n];
        }
        public static Modular Ncr(int n, int r)
        {
            return (n < r) ? 0
                 : (n == r) ? 1
                            : Fac(n) / (Fac(r) * Fac(n - r));
        }
        public static explicit operator int(Modular a)
        {
            return (int)a.value;
        }

        public static Modular Lcm(Modular a, Modular b)
        {
            var tmp = Gcdl(a.value, b.value);
            return ((a * b) / new Modular(tmp));
        }
        static Modular Gcd(Modular m, Modular n)
        {
            if (n.value > m.value) return Gcd(n, m);
            if (n.value == 0) return m;
            var r = new Modular(m.value % n.value);
            return Gcd(n, r);
        }

        static long Gcdl(long m, long n)
        {
            if (n > m) return Gcdl(n, m);
            if (n == 0) return m;
            return Gcdl(n, m % n);
        }
    }

}