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 Ruby (2.3.3) (judge verdict: Accepted)

require 'prime'

def common_divisors(n)
  return [1] if n == 1

  tmp = n.prime_division.map do |e|
    (0..e[1]).to_a.map do |i|
      e[0]**i
    end
  end

  tmp.reduce{|p,q| p.product(q)}.map do |a|
    [a].flatten.reduce(&:*)
  end.sort
end

n,m = gets.split.map(&:to_i)

divs =  common_divisors(m).reverse

divs.each do |d|
  if d * n <= m
    puts d
    exit
  end
end