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

C. Lucky Tickets

time limit per test

1.5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIn Walrusland public transport tickets are characterized by two integers: by the number of the series and by the number of the ticket in the series. Let the series number be represented by *a* and the ticket number — by *b*, then a ticket is described by the ordered pair of numbers (*a*, *b*).

The walruses believe that a ticket is lucky if *a* * *b* = *rev*(*a*) * *rev*(*b*). The function *rev*(*x*) reverses a number written in the decimal system, at that the leading zeroes disappear. For example, *rev*(12343) = 34321, *rev*(1200) = 21.

The Public Transport Management Committee wants to release *x* series, each containing *y* tickets, so that at least *w* lucky tickets were released and the total number of released tickets (*x* * *y*) were minimum. The series are numbered from 1 to *x* inclusive. The tickets in each series are numbered from 1 to *y* inclusive. The Transport Committee cannot release more than *max*_{x} series and more than *max*_{y} tickets in one series.

Input

The first line contains three integers *max*_{x}, *max*_{y}, *w* (1 ≤ *max*_{x}, *max*_{y} ≤ 10^{5}, 1 ≤ *w* ≤ 10^{7}).

Output

Print on a single line two space-separated numbers, the *x* and the *y*. If there are several possible variants, print any of them. If such *x* and *y* do not exist, print a single number - 1.

Examples

Input

2 2 1

Output

1 1

Input

132 10 35

Output

7 5

Input

5 18 1000

Output

-1

Input

48 132 235

Output

22 111

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/20/2017 13:48:55 (c4).

Desktop version, switch to mobile version.

User lists

Name |
---|