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())
i=0
l=[]
c=0
root=int(n**0.5)
for j in range(1,root+1):
    if n%j==0 and j*j!=n:
        l.append(j)
        l.append(int(n/j))
        c+=2
    elif j*j==n:    
        l.append(j)
        c+=1
l.sort()
if k>c:
    print(-1)
else:
    print(l[k-1])