Lucky Tickets

1000ms

262144K

Description:

In 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 ≤ 10⁵, 1 ≤ w ≤ 10⁷).

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.

Sample Input:

2 2 1

Sample Output:

1 1

Sample Input:

132 10 35

Sample Output:

7 5

Sample Input:

5 18 1000

Sample Output:

-1

Sample Input:

48 132 235

Sample Output:

22 111

Informação

Provedor Codeforces

Código CF70C