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 (2.7.6) (judge verdict: Accepted)

# B - K-th Common Divisor
# https://atcoder.jp/contests/abc120/tasks/abc120_b
# 1WA
MAX = 100

def gcd(m, n):
    return m if n == 0 else gcd(n, m % n)

A, B, K = map(int, raw_input().split())
gcdAB = gcd(A, B)

cnt = 0
for n in range(gcdAB, 0, -1):
    if gcdAB % n == 0:
        cnt += 1
        if cnt == K:
            print '{}'.format(n)
            break