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 Fortran (gfortran v4.8.4) (judge verdict: Runtime Error)

program main
implicit None
	integer(8)::n,m,a,i,k
	integer(8),allocatable::d(:)
	
	read *,n,m
	
	a = m/n
	allocate(d(a))
	
	k = 1
	
	do i = 1,a
		if(mod(m,i) == 0)then
			d(k) = i
			k = k+1
		endif
	enddo
	
	if(k /= 1)then
		k = k-1
	endif
	
	print 102,d(k)

101 format(a)
102 format(i0)
end program main