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
n,k=map(int,input().split())
k-=1
arr=[]
lim=int(math.sqrt(n))


for i in range(1,lim+1,1):
    if(n%i==0):
        if(int(n/i)==int(i)):
            arr.append(i)
        else:
            arr.append(i)
            arr.append(int(n/i))

if(len(arr)<=k):
    print("-1")
else:
    x=sorted(arr)
    print(x[k])