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)

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

require 'prime'

class Integer
  def my_divisor_list2
    return [1] if self == 1
    Prime.prime_division(self).map do |e|
      Array.new(e[1]+1).map.with_index do |element, i|
        e[0]**i
      end
    end.inject{|p,q| p.product(q)}.map do |a|
      [a].flatten.inject(&:*)
    end.sort
  end
end

a = m.my_divisor_list2
b = 1
a.each do |i|
  if i >= n
    b = i
    break
  end
end

puts m/b