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.