Codeforces Beta Round 64 |
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Finished |

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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 2010-2024 Mike Mirzayanov

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