| # 70_C. Lucky Tickets | |
| ## Problem 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 maxx series and more than maxy tickets in one series. | |
| Input | |
| The first line contains three integers maxx, maxy, w (1 ≤ maxx, maxy ≤ 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. | |
| 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 | |
| ## Contest Information | |
| - **Contest ID**: 70 | |
| - **Problem Index**: C | |
| - **Points**: 1500.0 | |
| - **Rating**: 2200 | |
| - **Tags**: binary search, data structures, sortings, two pointers | |
| - **Time Limit**: {'seconds': 1, 'nanos': 500000000} seconds | |
| - **Memory Limit**: 256000000 bytes | |
| ## Task | |
| Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases. |