TCS CodeVita | kth largest factor of N

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kth largest factor of N

Problem :

A positive integer d is said to be a factor of another positive integer N if when N is divided by d, the remainder obtained is zero. For example, for the number 12, there are 6 factors 1, 2, 3, 4, 6, 12. Every positive integer k has at least two factors, 1 and the number k itself.

Given two positive integers N and k, write a program to print the kth largest factor of N.

Input

The input is a comma separated list of positive integer pairs (N, k)

Output

The kth highest factor of N. If N does not have k factors, the output should be 1.

Constraints

1<N<10000000000. 1<k<600

You can assume that N will have no prime factors which are larger than 13.

Example 1

Input:

12,3

Output:

4

Explanation:

N is 12, k is 3. The factors of 12 are (1,2,3,4,6,12). The highest factor is 12 and the third largest factor is 4. The output must be 4

Example 2

Input:

30,9

Output:

1

Explanation:

N is 30, k is 9. The factors of 30 are (1,2,3,5,6,10,15,30). There are only 8 factors. As k is more than the number of factors, the output is 1.

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