//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

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

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, bytes) => {
        read_value!($iter, String).bytes().collect::<Vec<u8>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

//

fn pow_mod(r: u64, mut n: u64, m: u64) -> u64 {
    assert!(m > 0);
    if m == 1 {
        return 0;
    }
    let mut t = 1;
    let mut s = r % m;
    while n > 0 {
        if n & 1 == 1 {
            t = t * s % m;
        }
        s = s * s % m;
        n >>= 1;
    }
    t
}

fn factorize(mut n: u64) -> Vec<(u64, u64)> {
    let mut ans = vec![];
    for k in 2.. {
        if k * k > n {
            break;
        }
        let mut c = 0;
        while n % k == 0 {
            n /= k;
            c += 1;
        }
        if c > 0 {
            ans.push((k, c));
        }
    }
    if n > 1 {
        ans.push((n, 1));
    }
    ans
}

fn run() {
    input! {
        t: usize,
        ask: [u64; t],
    }
    for n in ask {
        let f = factorize(2 * n - 1);
        let phi = f.into_iter().fold(1, |s, (p, k)| s * (p - 1) * p.pow((k - 1) as u32));
        let mut ans = 2 * n - 1;
        for k in 1.. {
            if k * k > phi {
                break;
            }
            if phi % k == 0 {
                if pow_mod(2, k, 2 * n - 1) == 1 {
                    ans = std::cmp::min(ans, k);
                }
                if pow_mod(2, phi / k, 2 * n - 1) == 1 {
                    ans = std::cmp::min(ans, phi / k);
                }
            }
        }
        println!("{}", ans);
    }
}

fn main() {
    run();
}