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:
def fact(n):
    s=set()
    x=1
    while(x*x<=n):
        if(n%x==0):
            s.add(n//x)
            s.add(x)
        x+=1
    s=list(sorted(s))
    #print(s)
    return s
n,k=map(int,input().split())
l=fact(n)
if(k>len(l)):
    print(-1)
else:
    print(l[k-1])