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 Julia (0.5.0) (judge verdict: Wrong Answer)

function main()
	nm = parse.(split(readline()))
	q = nm[2]%nm[1]
	if q == 0
		print(Int(nm[2]/nm[1]))
	else
		k = (nm[2]-q)/nm[1]
		b = k%q
		if b == 0
			print(q)
		else
			if q%k == 0
				print(Int(q/k))
			elseif k%2 == q%2 && k > 1
				print(2)
			else
				print(1)
			end
		end
	end
end


main()