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 Rust (1.42.0) (judge verdict: Accepted)

// -*- coding:utf-8-unix -*-
use std::cmp;
use std::collections::BTreeMap;
use std::collections::BTreeSet;
use std::collections::BinaryHeap;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::LinkedList;
use std::collections::VecDeque;
use std::fs::File;
use std::io;
use std::io::prelude::*;

const INF: i64 = 1223372036854775807;

macro_rules! input {
    (source = s:expr, $(r:tt)*) => {
        let mut iter = s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $(r)*}
    };
    ($(r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $(r)*}
    };
}

macro_rules! input_inner {
    (next:expr) => {};
    (next:expr, ) => {};

    (next:expr, var:ident : t:tt $(r:tt)*) => {
        let var = read_value!(next, t);
        input_inner!{next $(r)*}
    };
}

macro_rules! read_value {
    (next:expr, ( $(t:tt),* )) => {
        ( $(read_value!(next, t)),* )
    };

    (next:expr, [ t:tt ; len:expr ]) => {
        (0..len).map(|_| read_value!(next, t)).collect::<Vec<_>>()
    };

    (next:expr, chars) => {
        read_value!(next, String).chars().collect::<Vec<char>>()
    };

    (next:expr, usize1) => {
        read_value!(next, usize) - 1
    };

    (next:expr, t:ty) => {
        next().parse::<t>().expect("Parse error")
    };
}

use std::cmp::*;
use std::collections::*;
use std::io::stdin;
use std::io::stdout;
use std::io::Write;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

/// Equivalent to std::lowerbound and std::upperbound in c++

fn solve() {
        let (n, p) = {
            let s = {
                let mut s = String::new(); // バッファを確保
                std::io::stdin().read_line(&mut s).unwrap(); // 一行読む。失敗を無視
                s.trim_right().to_owned() // 改行コードが末尾にくっついてくるので削る
            };
            
            let mut ws = s.split_whitespace(); // 空白区切りの単語に分解する
            let n: i32 = ws.next().unwrap().parse().unwrap(); // イテレータから値を取り出して整数に
            let m: i32 = ws.next().unwrap().parse().unwrap();
            (n, m)
        };
        let vec:Vec<i64> = read_vec();
        let mut dp :Vec<Vec<i64>> = vec![vec![0;(n+1)as usize];2];
        dp[0][0] = 1;
        for i in 0..(n) as usize {
            dp[0][i+1] += dp[0][i];
            dp[1][i+1] += dp[1][i];
            if vec[i]%2 == 1{
                dp[0][i+1] += dp[1][i];
                dp[1][i+1] += dp[0][i];
            }
            else {
                dp[0][i+1] += dp[0][i];
                dp[1][i+1] += dp[1][i];
            }
        }
        println!("{:?}", dp[p as usize][n as usize]);

    }
fn main() {
    solve()
}