10560: ABC120 —— B - K-th Common Divisor
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Description
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.
Find the $K$-th largest positive integer that divides both $A$ and $B$.
The input guarantees that there exists such a number.
Input
Input is given from Standard Input in the following format:
```
$A$ $B$ $K$
```
```
$A$ $B$ $K$
```
Output
Print the $K$-th largest positive integer that divides both $A$ and $B$.
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.
- $K \geq 1$
- $1 \leq A, B \leq 100$
- The $K$-th largest positive integer that divides both $A$ and $B$ exists.
- $K \geq 1$
Sample 1 Input
8 12 2
Sample 1 Output
2
Three positive integers divides both 8 and 12: 1,2 and 4. Among them, the second largest is 2.
Sample 2 Input
100 50 4
Sample 2 Output
5
Sample 3 Input
1 1 1
Sample 3 Output
1