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: Runtime Error)

require 'prime'

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

factors = Prime.prime_division(m)
nums = factors.map { |a, b| Array.new(b) { a } }.flatten
count = factors.map {|_, b| b}.inject(:+)
result = 1
count.downto(1).each do |i|
  list = nums.combination(i).to_a.uniq
  list.each do |ns|
    factor = ns.inject(:*)
    next if factor <= result
    rest = m / factor
    if rest >= n && factor > result
      result = factor
    end
  end
end
puts result