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=map(int,raw_input().split())
a=[]
b=[]
for i in range(1,int(n**0.5)+1):
	if n%i==0:
		a.append(i)
		if i**2!=n:
			b.append(n/i)
b.reverse()
if k>len(a)+len(b):
	print -1
elif k>len(a):
	print b[k-len(a)-1]
else:
	print a[k-1]