Problem: You are given two integers n and k. Find k-th smallest divisor of n, or report that it doesn't exist.

Divisor of n is any such natural number, that n can be divided by it without remainder.

Input

The first line contains two integers n and k (1 ≤ n ≤ 1015, 1 ≤ k ≤ 109).

Output

If n has less than k divisors, output -1.

Otherwise, output the k-th smallest divisor of n.

Examples

Input

4 2


Output

2


Input

5 3


Output

-1


Input

12 5


Output

6

Note

In the first example, number 4 has three divisors: 1, 2 and 4. The second one is 2.

In the second example, number 5 has only two divisors: 1 and 5. The third divisor doesn't exist, so the answer is -1.

Solution (in PYTHON):

Solution:
[n,k]=[int(i) for i in raw_input().split()]

x=1
fac=[]

while(x*x<=n):

	if(n%x==0):
		fac.append(x)

		if(n//x!=x):
			fac.append(n//x)
	x+=1

if(k<=len(fac)):
	fac.sort()
	print(fac[k-1])
else:
	print(-1)