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 Rust (1.15.1) (judge verdict: Accepted)

#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::io::{stderr, stdin, stdout, BufWriter, StdoutLock, Write};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[allow(unused_macros)]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut iter = $ s . split_whitespace ( ) ; let mut next = || { iter . next ( ) . unwrap ( ) } ; input_inner ! { next , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let mut bytes = std :: io :: Read :: bytes ( std :: io :: BufReader :: new ( stdin . lock ( ) ) ) ; let mut next = move || -> String { bytes . by_ref ( ) . map ( | r | r . unwrap ( ) as char ) . skip_while ( | c | c . is_whitespace ( ) ) . take_while ( | c |! c . is_whitespace ( ) ) . collect ( ) } ; input_inner ! { next , $ ( $ r ) * } } ; }
#[allow(unused_macros)]
macro_rules ! input_inner { ( $ next : expr ) => { } ; ( $ next : expr , ) => { } ; ( $ next : expr , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ next , $ t ) ; input_inner ! { $ next $ ( $ r ) * } } ; ( $ next : expr , mut $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let mut $ var = read_value ! ( $ next , $ t ) ; input_inner ! { $ next $ ( $ r ) * } } ; }
#[allow(unused_macros)]
macro_rules ! read_value { ( $ next : expr , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ next , $ t ) ) ,* ) } ; ( $ next : expr , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ next , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ next : expr , [ $ t : tt ] ) => { { let len = read_value ! ( $ next , usize ) ; ( 0 .. len ) . map ( | _ | read_value ! ( $ next , $ t ) ) . collect ::< Vec < _ >> ( ) } } ; ( $ next : expr , chars ) => { read_value ! ( $ next , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ next : expr , bytes ) => { read_value ! ( $ next , String ) . into_bytes ( ) } ; ( $ next : expr , usize1 ) => { read_value ! ( $ next , usize ) - 1 } ; ( $ next : expr , $ t : ty ) => { $ next ( ) . parse ::<$ t > ( ) . expect ( "Parse error" ) } ; }
#[allow(dead_code)]
struct Writer {
    s: String,
}
#[allow(unused_imports)]
use std::fmt::Display;
#[allow(dead_code)]
#[doc = " let mut writer = Writer::new();"]
#[doc = " writer.writeln(hoge);"]
#[doc = " writer.flush()"]
impl Writer {
    #[allow(dead_code)]
    pub fn new() -> Writer {
        Writer { s: String::new() }
    }
    #[allow(dead_code)]
    pub fn flush(&mut self) {
        print!("{}", self.s);
        self.s.clear();
    }
    pub fn write<T: Display>(&mut self, x: T) {
        self.s.push_str(&format!("{}", x));
    }
    pub fn writeln<T: Display>(&mut self, x: T) {
        self.s.push_str(&format!("{}", x));
        self.s.push('\n');
    }
    #[allow(dead_code)]
    pub fn write_vec<T: Display>(&mut self, xs: &Vec<T>) {
        if xs.len() == 0 {
            self.writeln("");
            return;
        }
        self.write(&format!("{}", xs[0]));
        for i in 1..xs.len() {
            self.write(&format!(" {}", xs[i]));
        }
        self.writeln("");
    }
}
#[allow(unused_macros)]
macro_rules ! dbg { ( $ ( $ a : expr ) ,* ) => { writeln ! ( & mut stderr ( ) , concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) . unwrap ( ) ; } }
#[allow(dead_code)]
pub const MOD: u64 = 1_000_000_007;
#[allow(dead_code)]
pub fn gcd(a: u64, b: u64) -> u64 {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}
#[allow(dead_code)]
pub fn lcm(a: u64, b: u64) -> u64 {
    a / gcd(a, b) * b
}
#[allow(dead_code)]
pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) {
    if b == 0 {
        (a, 1, 0)
    } else {
        let (gcd, x, y) = extgcd(b, a % b);
        (gcd, y, x - (a / b) * y)
    }
}
#[allow(dead_code)]
pub fn mod_pow(x: u64, n: u64, m: u64) -> u64 {
    let mut res = 1;
    let mut x = x % m;
    let mut n = n;
    while n > 0 {
        if n & 1 == 1 {
            res = (res * x) % m;
        }
        x = (x * x) % m;
        n >>= 1;
    }
    res
}
#[allow(dead_code)]
pub fn mod_inv(a: u64, m: u64) -> u64 {
    let (_, x, _) = extgcd(a as i64, m as i64);
    ((m as i64 + x) as u64 % m) % m
}
#[allow(dead_code)]
pub fn fact_table(size: usize, m: u64) -> Vec<u64> {
    let mut table = vec![1; size + 1];
    for i in 1..size + 1 {
        table[i] = (i as u64 * table[i - 1]) % m;
    }
    table
}
#[allow(dead_code)]
#[doc = " Factorial and Inverse factorial table"]
pub fn fact_inv_table(size: usize, m: u64) -> (Vec<u64>, Vec<u64>) {
    let mut fact = vec![1; size];
    let mut fact_inv = vec![1; size];
    for i in 2..size {
        fact[i] = fact[i - 1] * i as u64 % m;
        fact_inv[i] = m - ((m / i as u64) * fact_inv[(m % i as u64) as usize] % m);
    }
    for i in 1..size {
        fact_inv[i] = fact_inv[i - 1] * fact_inv[i] % m;
    }
    (fact, fact_inv)
}
#[allow(dead_code)]
pub fn mod_fact(n: u64, p: u64, fact: &[u64]) -> (u64, u64) {
    if n == 0 {
        (1, 0)
    } else {
        let (a, b) = mod_fact(n / p, p, fact);
        let pow = b + n / p;
        if n / p % 2 != 0 {
            (a * (p - fact[(n % p) as usize]) % p, pow)
        } else {
            (a * fact[(n % p) as usize] % p, pow)
        }
    }
}
#[allow(dead_code)]
#[doc = " C(n, k) % p"]
pub fn mod_comb(n: u64, k: u64, p: u64, fact: &[u64]) -> u64 {
    if n < k {
        0
    } else {
        let (a1, e1) = mod_fact(n, p, fact);
        let (a2, e2) = mod_fact(k, p, fact);
        let (a3, e3) = mod_fact(n - k, p, fact);
        if e1 > e2 + e3 {
            0
        } else {
            a1 * mod_inv(a2 * a3 % p, p) % p
        }
    }
}
#[allow(dead_code)]
#[doc = " H(n, k) % p"]
pub fn mod_comb_repetition(n: u64, k: u64, p: u64, fact: &[u64]) -> u64 {
    mod_comb(n - 1 + k, n - 1, p, fact)
}
#[allow(dead_code)]
fn main() {
    input! {
        a: u64,
        b: u64,
        c: usize
    }
    let mut x = Vec::new();
    for i in 1..101 {
        if a % i == 0 && b % i == 0 {
            x.push(i);
        }
    }
    x.reverse();
    println!("{}", x[c-1]);
}