#P762A. k-th divisor
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ID: 4361
Type: RemoteJudge
2000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> k-th divisor
No submission language available for this problem.
Description
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.
The first line contains two integers n and k (1 ≤ n ≤ 1015, 1 ≤ k ≤ 109).
If n has less than k divisors, output -1.
Otherwise, output the k-th smallest divisor of n.
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.
Samples
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.