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 C (GCC 5.4.1) (judge verdict: Accepted)

// AtCoder ABC120: B - K-th Common Divisor
// 2019.9.9 bal4u
// Template for Online Contest

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>

typedef long long ll;

#define gc() getchar()
#define pc(c) putchar(c)

int in() {  // 整数の入力
	int n = 0, c = gc();
	if (c == '-') {	c = gc();
		do n = 10*n + (c & 0xf), c = gc(); while (c >= '0');
		return -n;
	}
	do n = 10*n + (c & 0xf), c = gc(); while (c >= '0');
	return n;
}

ll inL() {  // long long 整数の入力
	ll n = 0; int c = gc();
	if (c == '-') {	c = gc();
		do n = 10*n + (c & 0xf), c = gc(); while (c >= '0');
		return -n;
	}
	do n = 10*n + (c & 0xf), c = gc(); while (c >= '0');
	return n;
}

void out(int n) { // 整数の表示
	int i; char b[30];
	if (!n) pc('0');
	else {
		if (n < 0) pc('-'), n = -n;
		i = 0; while (n) b[i++] = n % 10 + '0', n /= 10;
		while (i--) pc(b[i]);
	}
	pc('\n');
}

void outL(ll n) { // 整数の表示
	int i; char b[30];
	if (!n) pc('0');
	else {
		if (n < 0) pc('-'), n = -n;
		i = 0; while (n) b[i++] = n % 10 + '0', n /= 10;
		while (i--) pc(b[i]);
	}
	pc('\n');
}

int ins(char *s) { // 文字列の入力
	char *p = s--;
	do *++s = gc();
	while (*s > ' ');
	*s = 0;
	return s - p;
}

void outs(char *s) {  // 文字列の表示
	while (*s) pc(*s++);
}

#define MIN(a,b)  ((a)<=(b)?(a):(b))
#define MAX(a,b)  ((a)>=(b)?(a):(b))
#define ABS(a)    ((a)>=0?(a):-(a))
inline static int chmax(int *a, int b) { if (*a < b) *a = b; }
inline static ll  chmaxL(ll *a, int b) { if (*a < b) *a = b; }
inline static int chmin(int *a, int b) { if (*a > b) *a = b; }
inline static ll  chminL(ll *a, int b) { if (*a > b) *a = b; }

int cmp_int(const void *u, const void *v) { return *(int *)u - *(int *)v; }

int gcd(int a, int b)
{
	int r;
	while (b != 0) r = a % b, a = b, b = r;
	return a;
}

int main()
{
	int i, A, B, K, g;

	A = in(), B = in(), K = in();
	g = gcd(A, B);
	for (i = g; i >= 1; i--) if (g % i == 0) {
		if (--K == 0) break;
	}
	out(i);
	return 0;
}