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:
import math
ls=[]
ctr,f=0,1
n,k=map(int,input().split())
for i in range(1,math.ceil(math.sqrt(n))+1):
	if n%i==0:
		ls.append(i)
		ls.append(n//i)
		ctr+=1
	if ctr==k:
		f=0
		print(ls[-2])
		break
ls=list(set(ls))
if f:
    if len(ls)>=k:
        ls.sort()
        print(ls[k-1])
    else:
        print(-1)