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.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;


public class Main {
  public static void main(String[] args) {
    FastScanner sc = new FastScanner();
    int N = sc.nextInt();
    int P = sc.nextInt();
    int[] A = sc.nextIntList(N);

    long[][] dp = new long[2][N + 1];
    dp[0][0] = 1;
    for (int i = 0; i < N; i ++) {
      dp[0][i + 1] = dp[0][i];
      dp[1][i + 1] = dp[1][i];
      
      if (A[i] % 2 == 0) {
        dp[0][i + 1] += dp[0][i];
        dp[1][i + 1] += dp[1][i];
      } else {
        dp[0][i + 1] += dp[1][i];
        dp[1][i + 1] += dp[0][i];
      }
    }
    
    System.out.println(dp[P][N]);
  }
}


class FastScanner {
  public static String debug = null;

  private final InputStream in = System.in;
  private int ptr = 0;
  private int buflen = 0;
  private byte[] buffer = new byte[1024];
  private boolean eos = false;

  private boolean hasNextByte() {
    if (ptr < buflen) {
      return true;
    } else {
      ptr = 0;
      try {
        if (debug != null) {
          buflen = debug.length();
          buffer = debug.getBytes();
          debug = "";
          eos = true;
        } else {
          buflen = in.read(buffer);
        }
      } catch (IOException e) {
        e.printStackTrace();
      }
      if (buflen < 0) {
        eos = true;
        return false;
      } else if (buflen == 0) {
        return false;
      }
    }
    return true;
  }

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

  private static boolean isPrintableChar(int c) {
    return 33 <= c && c <= 126;
  }

  private void skipUnprintable() {
    while (hasNextByte() && !isPrintableChar(buffer[ptr]))
      ptr++;
  }

  public boolean isEOS() {
    return this.eos;
  }

  public boolean hasNext() {
    skipUnprintable();
    return hasNextByte();
  }

  public String next() {
    if (!hasNext())
      throw new NoSuchElementException();
    StringBuilder sb = new StringBuilder();
    int b = readByte();
    while (isPrintableChar(b)) {
      sb.appendCodePoint(b);
      b = readByte();
    }
    return sb.toString();
  }

  public long nextLong() {
    if (!hasNext())
      throw new NoSuchElementException();
    long n = 0;
    boolean minus = false;
    int b = readByte();
    if (b == '-') {
      minus = true;
      b = readByte();
    }
    if (b < '0' || '9' < b) {
      throw new NumberFormatException();
    }
    while (true) {
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
      b = readByte();
    }
  }

  public int nextInt() {
    return (int) nextLong();
  }

  public long[] nextLongList(int n) {
    return nextLongTable(1, n)[0];
  }

  public int[] nextIntList(int n) {
    return nextIntTable(1, n)[0];
  }

  public long[][] nextLongTable(int n, int m) {
    long[][] ret = new long[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        ret[i][j] = nextLong();
      }
    }
    return ret;
  }

  public int[][] nextIntTable(int n, int m) {
    int[][] ret = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        ret[i][j] = nextInt();
      }
    }
    return ret;
  }
}