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:
n,k=map(int,input().split())
l=[]
ans=-1
for i in range(1,n+1):
    if i*i>n:
        break
    if n%i==0:
        k-=1
        l.append(i)
    if k==0:
        ans=i
        break
if ans!=-1:
    print(ans)
else:
    if l[-1]*l[-1]==n:
        if k>len(l)-1:
            print(ans)
        else:
            print(n//l[len(l)-k-1])
    else:
        if k>len(l):
            print(ans)
        else:
            print(n//l[len(l)-k])