Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Multiplication Table

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBizon 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* ≤ 5·10^{5}; 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

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/24/2019 17:09:56 (f1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|