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: Runtime Error)

fn solve<R: BufRead, W: Write>(_reader: R, _writer: &mut W) {
  let mut _scanner = Scanner::new(_reader);

  #[allow(unused_macros)]
  macro_rules! scan {
    ($T:ty) => {
      _scanner.next::<$T>().unwrap()
    };
    ($($T:ty),+) => {
      ($(scan!($T)),+)
    };
    ($($T:ty),+; $n:expr $(; $m:expr)*) => {{
      let mut vec = Vec::with_capacity($n);
      for _ in 0..$n {
        vec.push(scan!($($T),+ $(; $m)*));
      }
      vec
    }};
  }

  #[allow(unused_macros)]
  macro_rules! scan_iter {
    ($T:ty; $n:expr) => {
      _scanner.take::<$T>($n).map(|x| x.unwrap())
    };
  }

  #[allow(unused_macros)]
  macro_rules! print {
    ($fmt:expr) => {
      write!(_writer, $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      write!(_writer, $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! println {
    ($fmt:expr) => {
      writeln!(_writer, $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      writeln!(_writer, $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! eprint {
    ($fmt:expr) => {
      #[cfg(debug_assertions)]
      write!(::std::io::stderr(), $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      #[cfg(debug_assertions)]
      write!(::std::io::stderr(), $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! eprintln {
    ($fmt:expr) => {
      #[cfg(debug_assertions)]
      writeln!(::std::io::stderr(), $fmt).unwrap()
    };
    ($fmt:expr, $($arg:tt)*) => {
      #[cfg(debug_assertions)]
      writeln!(::std::io::stderr(), $fmt, $($arg)*).unwrap()
    };
  }

  #[allow(unused_macros)]
  macro_rules! dump {
    ($($x:expr),+) => {
      eprint!("[{}:{}] ", file!(), line!());
      eprintln!(concat!($(stringify!($x), " = {:?}; "),+), $($x),+);
    };
  }

  use search::BinarySearch;

  let (n, m) = scan!(u64, u64);

  let mut cands = vec![];
  for x in 1..(m as f64).sqrt() as u64 {
    if m % x == 0 {
      cands.push(x);
    }
  }
  cands.reverse();
  dump!(cands);

  let i = BinarySearch::binary_search(&cands[..], |&x| {
    let r = x * n <= m;
    dump!(x, r);
    r
  }).unwrap();

  let ans = cands[i];
  println!("{}", ans);
}

const CUSTOM_STACK_SIZE_MEBIBYTES: Option<usize> = None;

fn main() {
  if let Some(stack_size_mebibytes) = CUSTOM_STACK_SIZE_MEBIBYTES {
    let builder = thread::Builder::new()
      .name("exec_solver".to_string())
      .stack_size(stack_size_mebibytes * 1024 * 1024);
    builder.spawn(exec_solver).unwrap().join().unwrap();
  } else {
    exec_solver();
  }
}

fn exec_solver() {
  let stdin = stdin();
  let stdout = stdout();
  #[cfg(debug_assertions)]
  let mut writer = stdout.lock();
  #[cfg(not(debug_assertions))]
  let mut writer = ::std::io::BufWriter::new(stdout.lock());
  solve(stdin.lock(), &mut writer);
  writer.flush().unwrap();
}

use io::Scanner;
use std::io::{stdin, stdout, BufRead, Write};
use std::thread;

pub mod misc {
  pub use self::byte_char::*;
  pub use self::byte_string::*;

  mod byte_char {
    use std::fmt::{self, Debug, Display, Formatter};

    #[derive(Clone, Copy, PartialOrd, Ord, PartialEq, Eq, Hash)]
    pub struct ByteChar(pub u8);

    impl Debug for ByteChar {
      fn fmt(&self, f: &mut Formatter) -> fmt::Result {
        write!(f, "b\'{}\'", self.0 as char)
      }
    }

    impl Display for ByteChar {
      fn fmt(&self, f: &mut Formatter) -> fmt::Result {
        write!(f, "{}", self.0 as char)
      }
    }
  }

  mod byte_string {
    use misc::ByteChar;
    use std::fmt::{self, Debug, Display, Formatter};

    #[derive(Clone, PartialOrd, Ord, PartialEq, Eq, Hash)]
    pub struct ByteString(pub Vec<ByteChar>);

    impl Debug for ByteString {
      fn fmt(&self, f: &mut Formatter) -> fmt::Result {
        write!(f, "b\"")?;
        for &c in &self.0 {
          write!(f, "{}", c.0 as char)?;
        }
        write!(f, "b\"")
      }
    }

    impl Display for ByteString {
      fn fmt(&self, f: &mut Formatter) -> fmt::Result {
        for &c in &self.0 {
          write!(f, "{}", c)?;
        }
        Ok(())
      }
    }
  }
}

pub mod io {
  pub use self::from_bytes::FromBytes;
  pub use self::scanner::Scanner;

  mod from_bytes {
    use misc::{ByteChar, ByteString};
    use std::str::{self, FromStr};

    #[derive(Debug)]
    pub struct FromBytesError;

    pub trait FromBytes: Sized {
      type Err;

      fn from_bytes(bytes: &[u8]) -> Result<Self, Self::Err>;
    }

    impl FromBytes for ByteChar {
      type Err = FromBytesError;

      fn from_bytes(bytes: &[u8]) -> Result<Self, Self::Err> {
        if bytes.len() == 1 {
          Ok(ByteChar(*unsafe { bytes.get_unchecked(0) }))
        } else {
          Err(FromBytesError)
        }
      }
    }

    impl FromBytes for ByteString {
      type Err = FromBytesError;

      fn from_bytes(bytes: &[u8]) -> Result<Self, Self::Err> {
        Ok(ByteString(bytes.iter().cloned().map(ByteChar).collect()))
      }
    }

    impl<T: FromStr> FromBytes for T {
      type Err = T::Err;

      fn from_bytes(bytes: &[u8]) -> Result<Self, Self::Err> {
        let s = if cfg!(debug_assertions) {
          str::from_utf8(bytes).unwrap()
        } else {
          unsafe { str::from_utf8_unchecked(bytes) }
        };
        T::from_str(s)
      }
    }
  }

  mod scanner {
    use io::FromBytes;
    use std::io::BufRead;
    use std::marker::PhantomData;

    pub struct Scanner<R> {
      reader: R,
      buffer: Vec<u8>,
      position: usize,
    }

    impl<R: BufRead> Scanner<R> {
      pub fn new(reader: R) -> Self {
        Scanner {
          reader: reader,
          buffer: vec![],
          position: 0,
        }
      }

      pub fn next<T: FromBytes>(&mut self) -> Result<T, T::Err> {
        FromBytes::from_bytes(self.next_bytes().unwrap_or(&[]))
      }

      pub fn take<T: FromBytes>(&mut self, n: usize) -> Take<R, T> {
        Take {
          scanner: self,
          n: n,
          _marker: PhantomData,
        }
      }

      pub fn next_bytes(&mut self) -> Option<&[u8]> {
        if self.buffer.is_empty() {
          self.read_line();
        }
        loop {
          match self.buffer.get(self.position) {
            Some(&b' ') => self.position += 1,
            Some(&b'\n') => self.read_line(),
            Some(_) => break,
            None => return None,
          }
        }
        let start = self.position;
        loop {
          match self.buffer.get(self.position) {
            Some(&b' ') | Some(&b'\n') | None => break,
            Some(_) => self.position += 1,
          }
        }
        Some(&self.buffer[start..self.position])
      }

      fn read_line(&mut self) {
        self.position = 0;
        self.buffer.clear();
        self.reader.read_until(b'\n', &mut self.buffer).unwrap();
      }
    }

    pub struct Take<'a, R: 'a, T> {
      scanner: &'a mut Scanner<R>,
      n: usize,
      _marker: PhantomData<fn() -> T>,
    }

    impl<'a, R: BufRead, T: FromBytes> Iterator for Take<'a, R, T> {
      type Item = Result<T, T::Err>;

      fn next(&mut self) -> Option<Self::Item> {
        if self.n > 0 {
          self.n -= 1;
          Some(self.scanner.next())
        } else {
          None
        }
      }

      fn size_hint(&self) -> (usize, Option<usize>) {
        (self.n, Some(self.n))
      }
    }

    impl<'a, R: BufRead, T: FromBytes> ExactSizeIterator for Take<'a, R, T> {}
  }
}

pub mod search {
  pub use self::binary_search::*;

  mod binary_search {
    use std::ops::Range;

    pub trait BinarySearch<T> {
      type Output;

      fn binary_search<F: FnMut(&T) -> bool>(&self, f: F) -> Option<Self::Output>;

      fn lower_bound(&self, x: &T) -> Option<Self::Output>
      where
        T: Ord,
      {
        self.binary_search(|t| t >= x)
      }

      fn upper_bound(&self, x: &T) -> Option<Self::Output>
      where
        T: Ord,
      {
        self.binary_search(|t| t > x)
      }

      fn lower_bound_by_key<B: Ord, F: FnMut(&T) -> B>(&self, x: B, mut f: F) -> Option<Self::Output> {
        self.binary_search(|t| f(t) >= x)
      }

      fn upper_bound_by_key<B: Ord, F: FnMut(&T) -> B>(&self, x: B, mut f: F) -> Option<Self::Output> {
        self.binary_search(|t| f(t) > x)
      }
    }

    macro_rules! binary_search_impl {
      ($ok:expr, $ng:expr, $cond1:expr, $cond2:expr) => {{
        let mut ok_end = $ok;
        let mut ng_start = $ng;
        while ok_end - ng_start > 1 {
          let mid = ng_start + (ok_end - ng_start) / 2;
          if $cond1(mid) {
            ok_end = mid;
          } else {
            ng_start = mid;
          }
        }
        if $cond2(ok_end) {
          None
        } else {
          Some(ok_end as Self::Output)
        }
      }};
    }

    impl<T> BinarySearch<T> for [T] {
      type Output = usize;

      fn binary_search<F: FnMut(&T) -> bool>(&self, mut f: F) -> Option<Self::Output> {
        binary_search_impl!(
          self.len() as isize,
          -1isize,
          |mid| f(&self[mid as usize]),
          |ok_end| ok_end as usize == self.len()
        )
      }
    }

    macro_rules! binary_search_impl_range {
          ($t:ty, $it:ty) => {
            impl BinarySearch<$t> for Range<$t> {
              type Output = $t;

              fn binary_search<F: FnMut(&$t) -> bool>(&self, mut f: F) -> Option<$t> {
                assert!(self.start <= self.end);
                binary_search_impl!(self.end as $it, self.start as $it - 1, |mid| f(&(mid as $t)), |ok_end| ok_end == self.end as $it)
              }
            }
          };
          ($($ut:ty, $it:ty);+) => {$(
            binary_search_impl_range! { $ut, $it }
            binary_search_impl_range! { $it, $it }
          )+};
        }

    binary_search_impl_range! { usize, isize; u32, i32; u64, i64 }
  }
}