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: Wrong Answer)

N,M = gets.strip.split.map(&:to_i)

require 'prime'

class Integer
  def my_divisor_list
    divisors = [1]
    primes = []
    Prime.prime_division(self).each do |prime|
      prime[1].times {primes << prime[0]}
    end

    1.upto(primes.size) do |i|
      primes.combination(i) do |prime|
        divisors << prime.inject{|a,b| a *= b}
      end
    end

    divisors.uniq!
    divisors.sort!
    return divisors
  rescue ZeroDivisionError
    return
  end
end

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

puts cnt