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 Ruby (2.3.3) (judge verdict: Accepted)

line = gets
line.chomp!

/(\d+)\s*(\d+)\s*(\d+)/ =~ line
a = $1.to_i
b = $2.to_i
k = $3.to_i

if a < b then
  c = a
  a = b
  b = c
end

def gcd (m,n)
  r = m % n
  m1 = m
  n1 = n
  # print m1, " % ", n1, " = ", r
  # puts ""
  while r > 0
    m1 = n1
    n1 = r
    r = m1 % n1
    # print m1, " % ", n1, " = ", r
    # puts ""
  end
  return n1
end

c = gcd(a,b)

count = 1

while count < k do
  c -= 1
  if a % c == 0 and b % c == 0
    count += 1
  end
end

print c