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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.lang.reflect.Array;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;


  public class Main {
	private InputStream is;
	private PrintWriter out;
	int time = 0, dp[][], DP[][], prime[], start[], parent[], end[], val[], black[], arr[], arr1[][];
	long  MOD = (long)(1e9+7);
	ArrayList<Integer>[] amp;
	boolean b[], b1[];
	Pair prr[];
	char ch[][],c[];
	HashSet<Integer> hs1 = new HashSet<>(), hs2 = new HashSet<>();

	public static void main(String[] args) throws Exception {
		new Thread(null, new Runnable() {
		public void run() {
			try {

		//new Main().soln();
		} catch (Exception e) {
				System.out.println(e);
			}
		}
	}, "1", 1 << 26).start();
		new Main().soln();
	}
	int MAX = 1000010, N, K, p = 1;
	PriorityQueue<Pair> pq;
	int Dp[][] = new int[1010][1010];
	void solve() {
		int n = ni(), p = ni();
		int arr[] = na(n);
		int e = 0, o = 0;
		for(int i:arr){
			if(i%2==0) e++;
			else o++;
		}
		long a = Math.round(Math.pow(2, e));
		long fact[][] = new long[o+1][o+1];
		for(int i = 0; i<=o;i++) fact[i][0] = 1;
		for(int i = 1;i<=o;i++){
			for(int j = 1;j<=i;j++){
				fact[i][j] = fact[i-1][j-1]+fact[i-1][j];
			}
		}
		long ans=0;
		if(p==0){
			for(int i = 0;i<=o;i+=2){
				ans += (fact[o][i]*a);
			}
		}
		else{
			for(int i = 1;i<=o;i+=2){
				ans += (fact[o][i]*a);
			}
		}
		System.out.println(ans);
	}
	class Node{
		Node left, right;
		int data;
		Node(int x){
			data = x;
		}
	}
	class BST{
		Node root;
		Node pre;
		void insert(int x){
			if(root==null){
				root = new Node(x);
				return;
			}
			Node temp = root;
			Node prev = temp;
			while(temp!=null){
				int y = temp.data;
				prev = temp;
				if(y>x) temp = temp.left;
				if(y<x) temp = temp.right;
			}
			if(prev.data>x) prev.left = new Node(x);
			else prev.right = new Node(x);
		}
		Node search(int x){
			Node temp = root;
			pre = null;
			while(temp!=null){
				int y = temp.data;
				if(y==x) return temp;
				pre = temp;
				if(y>x) temp = temp.left;
				if(y<x) temp = temp.right;
			}
			return null;
		}
		void delete(int x){
			Node n = search(x);
			if(n==null){
				System.out.println("No such element");
			}
			else if(n.left==null && n.right==null){
				if(pre!=null){
					if(pre.data>x) pre.left = null;
					else pre.right = null;
				}
				else root = null;
			}
			else if(n.left==null){
				while(n.right!=null){
					
				}
			}
			else if(n.right==null){
				
			}
			else{
				
			}
		}
		void inOrder(Node n){
			if(n==null) return;
			inOrder(n.left);
			System.out.print(n.data+"->");
			inOrder(n.right);
		}
	}
	void dfs(int x){
		//System.out.println(x+" "+hs1);
		boolean[] b = new boolean[arr1[x].length];
		for(int i = 0; i<arr1[x].length;i++){
			int val = arr1[x][i];
			if(val>0 && !hs1.contains(val)){
				hs1.add(val);
				b[i] = true;
			}
			else if(hs1.contains(val*-1)){
				hs1.remove(val*-1);
				b[i] = true;
			}
		}
		//System.out.println(x+" * "+hs1);
		end[x] = hs1.size();
		for(int i : amp[x])
			dfs(i);
		for(int i = 0; i<arr1[x].length; i++){
			if(b[i]){
				int val = arr1[x][i];
				if(val>0){
					if(hs1.contains(val)) hs1.remove(val);
				}
				else hs1.add(val*-1);
			}
		}
		//System.out.println(hs1+" "+x);
	}
	long[] mul(long arr[][], long temp[]){
		long ans[] = new long[temp.length];
		for(int i = 0; i<arr.length;i++){
			long sum = 0;
			for(int j = 0; j<arr.length;j++){
				sum = (sum+arr[i][j]*temp[j])%MOD;
			}
			ans[i] = sum;
		}
		return ans;
	}
	void printMat(long arr[][]){
		for(int i = 0; i< arr.length; i++){
			for(int j = 0; j < arr.length ;j++){
				System.out.print(arr[i][j]+" ");
			}
			System.out.println();
		}
		System.out.println("-----");
	}
	void printMat(long arr[]){
		for(int i = 0; i< arr.length; i++){
				System.out.print(arr[i]+" ");
		}
		System.out.println();
		System.out.println("-----");
	}
	long[][] matMul(int n, long arr[][], long y){
		long iden[][] = new long[n][n];
		for(int i= 0; i< n; i++) iden[i][i] = 1;
		//printMat(iden);
		while(y>0){
			if(y%2==1){
				iden = mul(n,iden,arr);
				//printMat(iden);
				y--;
			}
			else{
				arr = mul(n,arr,arr);
				//printMat(arr);
				y/=2;
			}
		}
		return iden;
	}
	long[][] mul(int n , long a1[][], long a2[][]){
		long temp[][] = new long[n][n];
		for(int i = 0; i< n; i++){
			for(int j = 0; j<n; j++){
				long sum = 0;
				for(int k = 0; k<n;k++){
					sum = (sum+a1[i][k]*a2[k][j])%MOD;
				}
				temp[i][j] = sum;
			}
		}
		return temp;
	}
	void seive(int n){
		b = new boolean[n+1];
		prime = new int[n+1];
		for(int i = 2;i*i<=n;i++){
			if(!b[i]){
				for(int j = 2*i; j<=n;j+=i){
					if(!b[j]){
						b[j] = true;
						prime[j] = i;
					}
				}
			}
		}
	}
	int binarySearch1(int arr[], int x){
		int ans = -1;
		int low = 0, high = arr.length-1;
		while(high>=low){
			int mid = (low+high)/2;
			if(arr[mid]>=x){
				ans = mid;
				high = mid-1;
			}
			else low = mid+1;
		}
		return ans;
	}
	int binarySearch2(Integer arr[], int x){
		int ans = -1;
		int low = 0, high = arr.length-1;
		while(high>=low){
			int mid = (low+high)/2;
			if(arr[mid]>=x){
				ans = mid;
				low = mid+1;
			}
			else high = mid-1;
		}
		return ans+1;
	}
	int cntEven(String str){
		int cnt = 0;
		for(int i = str.length()-1; i >= 0; i--){
			if((str.charAt(i)-'0')%2==0){
				cnt++;
			}
		}
		return cnt;
	}
	int max = 0;
	int getParent(int x){
		//System.out.println(x+" "+parent[x]);
		if(parent[x]!=x){
			parent[x] = getParent(parent[x]);
		}
		return parent[x];
	}
	class Pair implements Comparable<Pair>{
		int u;
		int v, r;
		Pair(int u, int v, int r){
			this.u = u;
			this.v = v;
			this.r = r;
		}
		Pair(int u, int v){
			this.u = u;
			this.v = v;
		}public int hashCode() {
			return Objects.hash();
		}
		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return ((u == other.u && v == other.v));// || (v == other.u && u == other.v));
		}
		public int compareTo(Pair other) {
			return Long.compare(u, other.u);
			//return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(v, other.v) != 0 ? (Long.compare(v, other.v)) :(Long.compare(other.r, r))) ;
		}	
		public String toString() {
			return "[u=" + u + ", v=" + v + "]";
		}
	}
	int min(int x,int y){
		if(x<y) return x;
		return y;
	}
	int max(int x,int y){
		if(x>y) return x;
		return y;
	}
	void buildGraph(int m){
		while(m-->0)
		{
			int x = ni()-1, y = ni()-1;
			amp[x].add(y);
			amp[y].add(x);
		}
	}
	long modInverse(long a, long mOD2){
        return  power(a, mOD2-2, mOD2);
	}
	long power(long x, long y, long m)
	{
		if (y == 0)
    return 1;
	long p = power(x, y/2, m) % m;
	p = (p * p) % m;

	return (y%2 == 0)? p : (x * p) % m;
	}
	boolean isPrime(int x){
		for(int i = 2;i*1L*i<=x;i++) if(x%i==0) return false;
		return true;
	}
	public long gcd(long a, long b){
		if(b==0) return a;
		return gcd(b,a%b);
	}
	void failFn(String str, int arr[]){
		int len = 0;
		arr[0] = 0;
		int i = 1;
		while(i<arr.length){
			if(str.charAt(i)==str.charAt(len)){
				arr[i++] = ++len;
				continue;
			}
			if(len == 0){
				arr[i] = len;
				i++;
				continue;
			}
			if(str.charAt(i)!=str.charAt(len)){
				len = arr[len-1];
			}
		}
	}
	static class ST1{
		int arr[], st[], size;
		ST1(int a[]){
			arr = a.clone();
			size = 10*arr.length;
			st = new int[size];
			build(0,arr.length-1,1);
		}
		void build(int ss, int se, int si){
			if(ss==se){
				st[si] = arr[ss];
				return;
			}
			int mid = (ss+se)/2;
			int val = 2*si;
			build(ss,mid,val); build(mid+1,se,val+1);
			st[si] = (st[val]+ st[val+1]);
		}
		int get(int ss, int se, int l, int r, int si){
			if(l>se || r<ss || l>r) return Integer.MAX_VALUE;
			if(l<=ss && r>=se) return st[si];
			int mid = (ss+se)/2;
			int val = 2*si;
			return (get(ss,mid,l,r,val)+ get(mid+1,se,l,r,val+1));
		}
	}
	static class ST{
		int arr[],lazy[],n;
		ST(int a){
			n = a;
			arr = new int[10*n];
			lazy = new int[10*n];
		}
		void up(int l,int r,int val){
			update(0,n-1,0,l,r,val);
		}
		void update(int l,int r,int c,int x,int y,int val){
			if(lazy[c]!=0){
				lazy[2*c+1]+=lazy[c];
				lazy[2*c+2]+=lazy[c];
				if(l==r)
					arr[c]+=lazy[c];
				lazy[c] = 0;
			}
			if(l>r||x>y||l>y||x>r)
				return;
			if(x<=l&&y>=r){
				lazy[c]+=val;
				return ;
			}
			int mid = l+r>>1;
			update(l,mid,2*c+1,x,y,val);
			update(mid+1,r,2*c+2,x,y,val);
			arr[c] = (arr[2*c+1]+ arr[2*c+2]);
		}
		int an(int ind){
			return ans(0,n-1,0,ind);
		}
		int ans(int l,int r,int c,int ind){
			if(lazy[c]!=0){
				lazy[2*c+1]+=lazy[c];
				lazy[2*c+2]+=lazy[c];
				if(l==r)
					arr[c]+=lazy[c];
				lazy[c] = 0;
			}
			if(l==r)
				return arr[c];
			int mid = l+r>>1;
			if(mid>=ind)
				return ans(l,mid,2*c+1,ind);
			return ans(mid+1,r,2*c+2,ind);
		}
	}
	public static class FenwickTree {
		
	    long[] array; // 1-indexed array, In this array We save cumulative information to perform efficient range queries and updates

	    public FenwickTree(int size) {
	        array = new long[size + 1];
	    }
	    public long rsq(int ind) {
	        assert ind > 0;
	        long sum = 0;
	        while (ind > 0) {
	            sum += array[ind];
	            //Extracting the portion up to the first significant one of the binary representation of 'ind' and decrementing ind by that number
	            ind -= ind & (-ind);
	        }
	        return sum;
	    }
	    public long rsq(int a, int b) {
	        assert b >= a && a > 0 && b > 0;
	        return rsq(b) - rsq(a - 1);
	    }
	    public void update(int ind, long value) {
	        assert ind > 0;
	        while (ind < array.length) {
	            array[ind] += value;
	            //Extracting the portion up to the first significant one of the binary representation of 'ind' and incrementing ind by that number
	            ind += ind & (-ind);
	        }
	    }
	    public int size() {
	        return array.length - 1;
	    }
	}
	public static int[] shuffle(int[] a, Random gen){
		for(int i = 0, n = a.length;i < n;i++)
		{ 
			int ind = gen.nextInt(n-i)+i; 
			int d = a[i]; 
			a[i] = a[ind];
			a[ind] = d; 
		} 
	return a; 
	}
	long power(long x, long y, int mod){
		long ans = 1;
		while(y>0){
			if(y%2==0){
				x = (x*x)%mod;
				y/=2;
			}
			else{
				ans = (x*ans)%mod;
				y--;
			}
		}
		return ans;
	}
	void soln() {
		is = System.in;
		out = new PrintWriter(System.out);
		long s = System.currentTimeMillis();
		solve();
		out.close();
		out.flush();
		tr(System.currentTimeMillis() - s + "ms");
	}


	// To Get Input
	// Some Buffer Methods
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

	private int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	private double nd() {
		return Double.parseDouble(ns());
	}

	private char nc() {
		return (char) skip();
	}
	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
									// ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

	private void tr(Object... o) {
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
}