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: Runtime Error)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;

public class Main {

	public static void main(String args[]) {
		FastScanner cin = new FastScanner(System.in);
		PrintWriter cout = new PrintWriter(System.out);
		solve(cin, cout);
		cout.flush();
	}

	private static void solve(FastScanner cin, PrintWriter cout) {
		assert solve(5, 1, 5, 2, 4);
		assert !solve(4, 7, 6, 4, 5);
		assert !solve(48792, 105960835, 681218449, 90629745, 90632170);
		assert solve(491995, 412925347, 825318103, 59999126, 59999339);

		int n = cin.nextInt();
		int a = cin.nextInt();
		int b = cin.nextInt();
		int c = cin.nextInt();
		int d = cin.nextInt();

		boolean ans = solve(n, a, b, c, d);
		if (ans)
			cout.println("YES");
		else
			cout.println("NO");
	}

	private static boolean solve(int n, int ia, int ib, int ic, int id) {
		long a = ia;
		long b = ib;
		long c = ic;
		long d = id;

		long dif = Math.abs(b - a);
		long rng = d - c;
		int moves = n - 1;
		int turns = moves / 2;
		for (int i = 0; i <= turns; i++) {
			long min = -rng * (turns - i) + c * i * 2;
			long max = +rng * (turns - i) + d * i * 2;
			if (moves % 2 == 1) {
				min += c;
				max += d;
			}
			if (min <= dif && dif <= max)
				return true;
		}
		return false;
	}

	static class FastScanner {
		private final InputStream in;
		private final byte[] buf = new byte[1 << 14];
		private int bufs = 0;
		private final long[] num = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 };
		private int ptr = 0;

		public FastScanner(InputStream in) {
			super();
			this.in = in;
		}

		boolean hasNext() {
			while (hasNextByte() && !isMeaningful(buf[ptr]))
				ptr++;
			return hasNextByte();
		}

		private boolean hasNextByte() {
			if (ptr < bufs)
				return true;
			ptr = 0;
			try {
				bufs = in.read(buf);
			} catch (IOException e) {
				throw new IllegalArgumentException(e);
			}
			if (bufs <= 0)
				return false;
			return true;
		}

		private static boolean isMeaningful(int b) {
			return 33 <= b && b <= 126;
			// return b != -1 && !Character.isWhitespace(b);
		}

		String next() {
			if (!hasNext())
				throw new IllegalArgumentException();
			StringBuilder sb = new StringBuilder();
			int b = read();
			while (isMeaningful(b)) {
				sb.appendCodePoint(b);
				b = read();
			}
			return sb.toString();
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		int nextInt() {
			long nl = nextLong();
			int ni = (int) nl;
			if (ni != nl)
				throw new IllegalArgumentException();
			return ni;
		}

		long nextLong() {
			if (!hasNext())
				throw new IllegalArgumentException();
			long n = 0;
			int plus = 1;
			int b = read();
			if (b == '-') {
				plus = -1;
				b = read();
			}
			if ('0' > b || b > '9')
				throw new java.lang.IllegalArgumentException();
			while (true) {
				if (!isMeaningful(b))
					return plus * n;
				n *= 10;
				n += num[b - '0'];
				b = read();
			}
		}

		private int read() {
			if (hasNextByte())
				return buf[ptr++];
			else
				return -1;
		}

	}
}