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: Accepted)

A, B, K = map(int, input().split())
a=[]
#b=[]
if A>=B:
  for i in range(1, A+1): # i = [1,2,3,4,....A]
    if A%i==0 and B%i==0:
      a.append( i )
      # b.append( B/i )
  
else:
  for i in range(1, B+1): # i = [1,2,3,4,....A]
    if A%i==0 and B%i==0:
      a.append( i )
      # b.append( B/i )

#print(a)
#print(b)

#c=[]
#for ea in a:
 # if ea in b:
  #  c.append( ea )
c=len(a)
print(a[c-K])