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 divisors(n):
    res = []
    for i in range(1,int(n**0.5)+1):
        if n%i==0:
            res.append(i)
            res.append(n//i)
    return res
n,k = map(int,input().split())
arr = divisors(n)
arr = sorted(set(arr))
count = 0
for i in arr:
    if count==k-1:
        print(i)
        break
    count+=1
else:
    print(-1)