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762A · k-th divisor

1400 · math, number theory

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

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

Otherwise, output the k-th smallest divisor of n.

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.

Sample Cases

Case 1

Input

4 2

Output

2

Case 2

Input

5 3

Output

-1

Case 3

Input

12 5

Output

6

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