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 PYTHON3):

Solution:
from math import sqrt
import copy
a=input()
b=a.split()
n=int(b[0])
k=int(b[1])
x=int(sqrt(n))
a=[]
for y in range(1,x+1):
 if (n%y==0):
 	a.append(y)
b=copy.deepcopy(a)
if (len(b)>=k):
	print (a[k-1])

else:
	c=len(b)
	o=0
	for j in range(len(b)-1,-1,-1):
		r=n//b[j]
		if (r!=b[j]):
			c+=1
			if (c==k):
				print (r)
				o=1
				break
	if (o==0):
		print (-1)