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 (1.15.1) (judge verdict: Wrong Answer)

//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
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")
    };
}

pub struct Combination {
    stack: Vec<usize>,
}

impl Combination {
    pub fn new(number: usize) -> Self {
        const MODULO: usize = 1000000007;
        let mut stack: Vec<usize> = Vec::new();
        stack.push(1);
        for i in 0..number {
            let k = (stack[i] * (number - i) % MODULO) * ModInv::mod_inv(i as isize + 1, MODULO) % MODULO;
            stack.push(k);
        }

        Combination {
            stack: stack,
        }
    }

    pub fn get(&self, number: usize) -> usize {
        self.stack[number]
    }
}

use std::mem::swap;

struct ModInv {}

impl ModInv {
    pub fn mod_inv(number: isize, modulo: usize) -> usize {
        let mut n = number;
        let mut b = modulo as isize;
        let mut u: isize = 1;
        let mut v: isize = 0;

        while b > 0 {
            let t: isize = n / b;
            n -= t * b;
            swap(&mut n, &mut b);
            u -= t * v;
            swap(&mut u, &mut v);
        }
        u %= modulo as isize;
        if u < 0 {
            u += modulo as isize;
        }
        u as usize
    }
}


fn main()
{
    input! {
        n:usize,
        p:usize,
        v: [i32; n]
    }
    let mut odds: usize = 0;
    let mut evens: usize = 0;

    for vi in v {
        odds += vi as usize % 2;
        evens += (1 + vi as usize % 2) % 2;
    }

    let odd_comb = Combination::new(odds);
    let even_comb = Combination::new(evens);

    let ans = (0..odds+1 as usize).collect::<Vec<usize>>()
        .iter()
        .filter(|odd| *odd % 2 == p)
        .map(|odd| (0..evens+1 as usize).collect::<Vec<usize>>()
            .iter()
            .map(|even| odd_comb.get(*odd) * even_comb.get(*even))
            .sum::<usize>()
        ).sum::<usize>();
    println!("{}", ans);
}