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: Accepted)

fn main() {
    let mut input_buffer = String::with_capacity(cpio::BUFFER_SIZE);
    let mut output_buffer = Vec::with_capacity(cpio::BUFFER_SIZE);
    unsafe {
        cpio::input::buf = &mut output_buffer;
        cpio::output::buf = &mut input_buffer;
    }
    std::thread::Builder::new()
        .stack_size(104_857_600)
        .spawn(solve)
        .unwrap()
        .join()
        .unwrap();
    cpio::output::flush();
}

#[macro_use]
#[allow(dead_code, non_upper_case_globals, unused_macros)]
mod cpio {
    pub const BUFFER_SIZE: usize = 8192;
    #[macro_use]
    pub mod output {
        pub const ENABLE_DUMP: bool = true;
        pub const PRECISION: usize = 10;
        pub static mut buf: *mut String = 0 as *mut String;

        macro_rules! p {
            ($x: expr) => {{
                $x.output();
                '\n'.output();
                unsafe {
                    if (*cpio::output::buf).len() > cpio::BUFFER_SIZE {
                        flush();
                    }
                }
            }};
            ($x: expr, $($y: expr),+) => {{
                $x.output();
                ' '.output();
                p!($($y),+);
            }};
        }

        macro_rules! pf {
            ($($x: expr),+) => {{
                p!($($x),+);
                flush();
            }};
        }

        macro_rules! d {
            ($($a: expr),+) => {
                if ENABLE_DUMP {
                    use std::io::*;
                    write!(stderr(), "{}:{}\t", file!(), line!()).unwrap();
                    d!(A $($a),+);
                    write!(stderr(), " = ").unwrap();
                    d!(B $($a),+);
                    write!(stderr(), "\n").unwrap();
                    stderr().flush().unwrap();
                }
            };
            (A $x: expr) => {
                write!(stderr(), "{}", stringify!($x)).unwrap();
            };
            (A $x: expr, $($y: expr),+) => {
                write!(stderr(), "{}, ", stringify!($x)).unwrap();
                d!(A $($y),+);
            };
            (B $x: expr) => {
                write!(stderr(), "{:?}", $x).unwrap();
            };
            (B $x: expr, $($y: expr),+) => {
                write!(stderr(), "{:?}, ", $x).unwrap();
                d!(B $($y),+);
            };
        }

        pub trait Output {
            fn output(&self);
        }

        macro_rules! output_normal {
            ($t: ty) => {
                impl Output for $t {
                    fn output(&self) {
                        unsafe {
                            use std::fmt::Write;
                            write!(&mut *buf, "{}", self).unwrap();
                        }
                    }
                }
            };
            ($t: ty, $($u: ty),+) => {
                output_normal!($t);
                output_normal!($($u),+);
            };
        }

        macro_rules! output_float {
            ($t: ty) => {
                impl Output for $t {
                    fn output(&self) {
                        unsafe {
                            use std::fmt::Write;
                            write!(&mut *buf, "{:.*}", PRECISION, self).unwrap();
                        }
                    }
                }
            };
            ($t: ty, $($u: ty),+) => {
                output_float!($t);
                output_float!($($u),+);
            };
        }

        pub fn flush() {
            unsafe {
                print!("{}", *buf);
                use std::io::*;
                stdout().flush().unwrap();
                (*buf).clear();
            }
        }

        output_normal!(u8, u16, u32, u64, usize, char);
        output_normal!(i8, i16, i32, i64, isize);
        output_normal!(bool, &'static str, String);
        output_float!(f32, f64);
    }

    pub mod input {
        pub trait Input<T> {
            fn input() -> T;
        }

        macro_rules! input_primitive {
            ($t: ty) => {
                impl Input<$t> for $t {
                    fn input() -> $t {
                        get_word().parse()
                            .unwrap_or_else(|e| panic!("Parse error : {}", e))
                    }
                }
            };
            ($t: ty, $($u: ty),+) => {
                input_primitive!($t);
                input_primitive!($($u),+);
            };
        }

        macro_rules! input_tuple {
            ($($t: ident),*) => {
                impl< $($t: Input<$t>),* > Input< ( $($t),* ) > for ( $($t),* ) {
                    fn input() -> ( $($t),* ) {
                        ( $( $t::input()),* )
                    }
                }
            };
        }

        input_primitive!(u8, u16, u32, u64, usize);
        input_primitive!(i8, i16, i32, i64, isize);
        input_primitive!(bool, String);
        input_tuple!(A, B);
        input_tuple!(A, B, C);
        input_tuple!(A, B, C, D);

        pub fn get<T: Input<T>>() -> T {
            T::input()
        }

        pub fn get_vec<T: Input<T>>(n: usize) -> Vec<T> {
            (0..n).map(|_| get()).collect()
        }

        pub fn get_mat<T: Input<T>>(r: usize, c: usize) -> Vec<Vec<T>> {
            (0..r).map(|_| get_vec(c)).collect()
        }

        pub fn get_vec_char() -> Vec<char> {
            Reader.skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        }

        pub fn get_mat_char(h: usize) -> Vec<Vec<char>> {
            (0..h).map(|_| get_vec_char()).collect()
        }

        fn get_word() -> String {
            Reader.skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        }

        pub fn has_next() -> bool {
            if let Some(c) = Reader.skip_while(|c| c.is_whitespace()).next() {
                unget(c as u8);
                true
            } else {
                false
            }
        }

        pub static mut buf: *mut Vec<u8> = 0 as *mut Vec<u8>;
        static mut buf_slice: [u8; super::BUFFER_SIZE] = [0; super::BUFFER_SIZE];

        struct Reader;
        impl Iterator for Reader {
            type Item = char;
            fn next(&mut self) -> Option<Self::Item> {
                unsafe {
                    use std::io::{stdin, Read};
                    let b = &mut (*buf);
                    if b.is_empty() {
                        if let Ok(l) = stdin().read(&mut buf_slice) {
                            for i in (0..l).rev() {
                                b.push(buf_slice[i]);
                            }
                        }
                    }
                    b.pop().map(|c| c as char)
                }
            }
        }

        fn unget(c: u8) {
            unsafe { (*buf).push(c) }
        }
    }
}

#[allow(unused_imports)]
use cpio::input::*;
#[allow(unused_imports)]
use cpio::output::*;

fn solve() {
    while has_next() {
        let (n, p): (_, usize) = get();
        let even = (0..n).map(|_| get::<i64>()).filter(|&x| x % 2 == 0).count();
        let odd = (n - even) as i64;
        let ans = if odd == 0 {
            if p == 0 {
                1u64 << n
            } else {
                0
            }
        } else {
            1u64 << (n - 1)
        };
        p!(ans);
    }
}