Bizon the Champion isn't just charming, he also is very smart.

While some of us were learning the multiplication table, Bizon the Champion had fun in his own manner. Bizon the Champion painted an n × m multiplication table, where the element on the intersection of the i-th row and j-th column equals i·j (the rows and columns of the table are numbered starting from 1). Then he was asked: what number in the table is the k-th largest number? Bizon the Champion always answered correctly and immediately. Can you repeat his success?

Consider the given multiplication table. If you write out all n·m numbers from the table in the non-decreasing order, then the k-th number you write out is called the k-th largest number.

Input

The single line contains integers n, m and k (1 ≤ n, m ≤ 5·105; 1 ≤ k ≤ n·m).

Output

Print the k-th largest number in a n × m multiplication table.

Examples

Input

2 2 2


Output

2


Input

2 3 4


Output

3


Input

1 10 5


Output

5

Note

A 2 × 3 multiplication table looks like this:
    
    
      
    1 2 3  
    2 4 6  
      
    
import java.io.*;
import java.util.*;

public class Main {
    static FastScanner in;
    static long arr[][];

    public static void main(String[] args) throws IOException {
        // System.setOut(new PrintStream(new BufferedOutputStream(new FileOutputStream("output.out")), true)); 
        in = new FastScanner(System.in);
        //        in = new FastScanner("input.txt");
        long n = in.nextLong();
        long m = in.nextLong();
        long k = in.nextLong();
        long l = 1;
        long r = n * m + 1;
        while (l < r) {
            long mm = (l + r) / 2;
            if (check(n, m, mm) < k) {
                l = mm + 1;
            } else {
                r = mm;
            }
        }
        System.out.println(l - 1);
    }

    static long check(long n, long m, long mm) {
        mm--;
        long ans = 0;
        for (long i = 1; i <= n; i++) {
            ans += Math.min(m, mm / i);
        }
        return ans;
    }
}

class FastScanner {

    BufferedReader br;
    StringTokenizer tokenizer;

    FastScanner(String fileName) throws FileNotFoundException {
        this(new FileInputStream(new File(fileName)));
    }

    FastScanner(InputStream is) {
        br = new BufferedReader(new InputStreamReader(is));
    }

    String nextLine() throws IOException {
        tokenizer = null;
        return br.readLine();
    }

    String next() throws IOException {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            String line = br.readLine();
            if (line == null) {
                return null;
            }
            tokenizer = new StringTokenizer(line);
        }
        return tokenizer.nextToken();
    }

    int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    char nextChar() throws IOException {
        return next().charAt(0);
    }
}