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 = STDIN.gets.chomp.split(/ +/).map(&:to_i)

ret = 0

if m % n == 0
  ret = m / n
else

	divider = []
	
	mm = m
	
	i = 2
	maxDiv = 0
  while mm >= Math.sqrt(m) do
	    if mm % i == 0
	      if i >= n
	      	maxDiv = i
	      	break
	      end
	      mm /= i
	    end
	    i += 1
	end
  
  if maxDiv == 0 
    maxDiv = m
  end
  
	ret = m / maxDiv

end

puts ret