Problem:
Score : 400 points

Problem Statement

You are given integers N and M.

Consider a sequence a of length N consisting of positive integers such that a_1 + a_2 + ... + a_N = M. Find the maximum possible value of the greatest common divisor of a_1, a_2, ..., a_N.

Constraints

All values in input are integers.

1 \leq N \leq 10^5

N \leq M \leq 10^9

Input

Input is given from Standard Input in the following format:

N M

Output

Print the maximum possible value of the greatest common divisor of a sequence a_1, a_2, ..., a_N that satisfies the condition.

Sample Input 1

3 14

Sample Output 1

2

Consider the sequence (a_1, a_2, a_3) = (2, 4, 8). Their greatest common divisor is 2, and this is the maximum value.

Sample Input 2

10 123

Sample Output 2

3

Sample Input 3

100000 1000000000

Sample Output 3

10000

Solution in Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use template::buf_scan::*;
#[allow(unused_imports)]
use template::*;

#[allow(dead_code)]
#[macro_use]
pub mod macros {
    #[macro_export]
    macro_rules! debug {
        ($($a:expr),*) => {{
            use ::std::io::Write;
            writeln!(&mut ::std::io::stderr(), concat!($(stringify!($a), " = {:?}, "),*), $($a),*).unwrap();
        }}
    }

    #[macro_export]
    macro_rules! input {
        (source = $s:expr, $($r:tt)*) => {
            let mut scanner = $crate::template::buf_scan::BufScanner::new($s.as_bytes());
            input_inner!{scanner, $($r)*}
        };
        ($($r:tt)*) => {
            let stdin = ::std::io::stdin();
            let mut scanner = $crate::template::buf_scan::BufScanner::new(stdin.lock());
            input_inner!{scanner, $($r)*}
        };
    }

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

    macro_rules! read_value {
        ($scanner:ident, ( $($t:tt),* )) => {
            ( $(read_value!($scanner, $t)),* )
        };
        ($scanner:ident, [ $t:tt ; $len:expr ]) => {
            (0..$len).map(|_| read_value!($scanner, $t)).collect::<Vec<_>>()
        };
        ($scanner:ident, chars) => {
            read_value!($scanner, String).chars().collect::<Vec<char>>()
        };
        ($scanner:ident, usize1) => {
            read_value!($scanner, usize) - 1usize
        };
        ($scanner:ident, $t:ty) => {
            ($scanner).next::<$t>()
        };
    }
}

fn main() {
    input! {
        n: u32,
        m: u32,
    }
    let mut res = 1;
    let m: u32 = m;
    let s = (m as f64).sqrt() as u32 + 10;
    for i in (1..s).filter(|x| m % x == 0) {
        let a = i;
        let b = m / a;
        if a >= n {
            res = std::cmp::max(res, b);
        }
        if b >= n {
            res = std::cmp::max(res, a);
        }
    }
    println!("{}", res);
}

#[allow(dead_code)]
pub mod template {
    pub mod buf_scan {
        pub struct BufScanner<R: ::std::io::BufRead> {
            br: R,
            buf: Vec<u8>,
            pos: usize,
        }

        impl<R: ::std::io::BufRead> BufScanner<R> {
            pub fn new(br: R) -> Self {
                BufScanner {
                    br: br,
                    buf: Vec::new(),
                    pos: 0usize,
                }
            }
            fn fill_line(&mut self) {
                self.buf.clear();
                self.pos = 0;
                self.br
                    .read_until(b'\n', &mut self.buf)
                    .expect("Read a line");
                if let Some(&b'\n') = self.buf.last() {
                    self.buf.pop();
                    if let Some(&b'\r') = self.buf.last() {
                        self.buf.pop();
                    }
                }
            }
            fn skip_space(&mut self) {
                loop {
                    for i in self.pos..self.buf.len() {
                        if self.buf[i] != b' ' {
                            self.pos = i;
                            return;
                        }
                    }
                    self.fill_line();
                }
            }
            pub fn read_token(&mut self) -> &str {
                self.skip_space();
                let start = self.pos;
                while self.pos < self.buf.len() && self.buf[self.pos] != b' ' {
                    self.pos += 1;
                }
                let ret = unsafe { ::std::str::from_utf8_unchecked(&self.buf[start..self.pos]) };
                self.pos += 1; // skip the last space (or len() + 1 which is fine)
                return ret;
            }
            pub fn next<T: ::std::str::FromStr>(&mut self) -> T {
                self.read_token().parse::<T>().ok().expect("Parse")
            }
        }
    }
}