Problem:
Score : 400 points

Problem Statement

There are N empty boxes arranged in a row from left to right.
The integer i is written on the i-th box from the left (1 \leq i \leq N).

For each of these boxes, Snuke can choose either to put a ball in it or to put nothing in it.

We say a set of choices to put a ball or not in the boxes is good when the following condition is satisfied:

For every integer i between 1 and N (inclusive), the total number of balls contained in the boxes with multiples of i written on them is congruent to a_i modulo 2.

Does there exist a good set of choices? If the answer is yes, find one good set of choices.

Constraints

All values in input are integers.

1 \leq N \leq 2 \times 10^5

a_i is 0 or 1.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

If a good set of choices does not exist, print -1.

If a good set of choices exists, print one such set of choices in the following format:

M
b_1 b_2 ... b_M

where M denotes the number of boxes that will contain a ball, and b_1,\ b_2,\ ...,\ b_M are the integers written on these boxes, in any order.

Sample Input 1

3
1 0 0

Sample Output 1

1
1

Consider putting a ball only in the box with 1 written on it.

There are three boxes with multiples of 1 written on them: the boxes with 1, 2, and 3. The total number of balls contained in these boxes is 1.

There is only one box with a multiple of 2 written on it: the box with 2. The total number of balls contained in these boxes is 0.

There is only one box with a multiple of 3 written on it: the box with 3. The total number of balls contained in these boxes is 0.

Thus, the condition is satisfied, so this set of choices is good.

Sample Input 2

5
0 0 0 0 0

Sample Output 2

0

Putting nothing in the boxes can be a good set of choices.

Solution in Rust (1.15.1) (judge verdict: Runtime Error)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}



fn main() {
    let v = read_vec::<usize>();
    let (n, k) = (v[0], v[1]);
    let big_int = 1000_000_000 + 7;

    if n == 1 {
        if k == 0 {
            println!("1");
        } else {
            println!("0");
        }
        return;
    }

    let mut dp = vec![vec![0; k + 1]; 1 << (n / 2)];
    dp[0][0] = 1;
    for S in (1..dp.len()) {
        for v in 0..k + 1 {
            for u in 0..n / 2 {
                if (S >> u) & 1 == 0 {
                    dp[S | 1 << u][v] += dp[S][v];
                    dp[S | 1 << u][v] %= big_int;
                }
            }
        }
    }

    let mut dp2 = vec![vec![0; k + 1]; 1 << (n - (n / 2))];
    dp2[0][0] = 1;
    for S in (1..dp2.len()) {
        for v in 0..k + 1 {
            for u in 0..(n - n / 2) {
                if (S >> u) & 1 == 0 {
                    dp2[S | 1 << u][v] += dp2[S][v];
                    dp2[S | 1 << u][v] %= big_int;
                }
            }
        }
    }

    let mut ans = 0i64;

    for i in 0..k + 1 {
        let mut temp = dp[1 << (n / 2) - 1][i] + dp2[1 << (n - (n / 2)) - 1][k - i];
        temp %= big_int;
        ans += temp;
        ans %= big_int;
    }
    println!("{}", ans);
}

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()
}