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.strip.split.map(&:to_i)

require 'prime'

class Integer
  def my_divisor_list3
    return [1] if self == 1
    first, *rest = Prime.prime_division(self).map do |p, k|
      (0..k).map{|i| p**i}
    end
    first.product(*rest).map do |a|
      a.inject(&:*)
    end.sort
  end
end

i = 0
x = M.my_divisor_list3
cnt = M
if N == 1
else
  while x[i] <= M
    if x[i] > (M/N)
      cnt = x[i - 1]
      break
    end
    i += 1
  end
end

puts cnt