Problem:
Score : 200 points

Problem Statement

You are given positive integers A and B.

Find the K-th largest positive integer that divides both A and B.

The input guarantees that there exists such a number.

Constraints

All values in input are integers.

1 \leq A, B \leq 100

The K-th largest positive integer that divides both A and B exists.

K \geq 1

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the K-th largest positive integer that divides both A and B.

Sample Input 1

8 12 2

Sample Output 1

2

Three positive integers divides both 8 and 12: 1, 2 and 4.
Among them, the second largest is 2.

Sample Input 2

100 50 4

Sample Output 2

5

Sample Input 3

1 1 1

Sample Output 3

1

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

A, B, K = [int(akb) for akb in input().split()]
a, b = min(A, B), max(A, B)
r = b % a
while r > 0:
  b = a
  a = r
  r = b % a
gcd = a
ans = a
if K > 1:
  for i in range(1, 100):
    if gcd % (i+1) == 0:
      ans = gcd / (i+1)
      K -= 1
    if K == 1:
      break
print(ans)