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:
'''input
12 5
'''
import math
from fractions import gcd
def mp():
	return map(int,str(raw_input()).split())
mod=10**9+7 
n,k=mp()
k-=1
a=[]
for i in range(1,int(math.sqrt(n))+1):
	if n%i==0:
		if n/i==i:
			a.append(i)
		else:
			a.append(i)
			a.append(n/i)
a.sort()
if k>=len(a):
	print -1
else:
	print a[k]