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: Time Limit Exceeded)

require 'prime'

n, m = gets.split.map(&:to_i)
divisions = m.prime_division
opts = []
divisions.each do |d, count|
  count.times { opts << d }
end
divisor = m
size = opts.size
(2 ** size).times do |i|
  product = 1
  size.times do |bit|
    product *= opts[bit] if i[bit] == 1
    break if divisor <= product
  end
  divisor = product if n <= product && divisor > product
end
puts m / divisor