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 divisor_list
    return [] if self <= 0
    return [1] if self == 1
    prime_division.map{|e| [*(0..e.last)].map{|v| e.first ** v }}.inject{|res, e| res.map{|t| e.map{|v| t * v}}.flatten}.sort
  end
end
class Array
  def upper_bound(val)
    a = 0
    b = size
    while a < b
      c = (( a + b ) / 2 ).to_i
      if val < at(c)
        b = c
      else
        a = c + 1
      end
    end
    b
  end
  def lower_bound(val)
    a = 0
    b = size
    while a < b
      c = (( a + b ) / 2 ).to_i
      if val <= at(c)
        b = c
      else
        a = c + 1
      end
    end
    b
  end
end
p M.divisor_list.select{|x|x*N<=M}[-1]