Educational Codeforces Round 17-A k-th divisor

You are given two integers n and k. Find k-th smallest divisor ofn, or report that it doesn't exist.

Divisor of n is any such natural number, thatn can be divided by it without remainder.

Input

The first line contains two integers n andk (1 ≤ n ≤ 10¹⁵,1 ≤ k ≤ 10⁹).

Output

If n has less than k divisors, output -1.

Otherwise, output the k-th smallest divisor ofn.

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.

给一个数N，找到第K个能被N整除的数，如果找不到，则输出-1. 遍历因子到sqrt（n）