eolymp
bolt
Try our new interface for solving problems
Problems

Forest dwellers

Forest dwellers

Time limit 1 second
Memory limit 64 MiB

Forest dwellers known to you at problems "Play hockey real...", finally had conceived their hockey tournament round-robin in a circle, ie Each team played each one meeting. It is known that as is often the stage of the competition, the fans were unhappy with the refereeing every match, so each match is assigned a new judge from the number of those same fans. Fans, as the players were all living in the forest, forest dwellers. Players, regardless of whether they participate in a particular game or not, can not be appointed as a judge of any meeting, because they are interested. Knew the total number of forest dwellers k, and the fact that in each of n teams plays m players. If the next meeting it was impossible to assign a new judge, then such a meeting is recognized as a draw, while in meetings played anybody did not exist, since in this extreme case, the winner is determined at the end of the meeting in shoot-out.

Need to find a number of successful draws and meetings held in the forest inhabitants hockey tournament.

Input data

In a single line separated by spaces given three numbers, respectively, k, n and m. All numbers are positive and do not exceed 2∙10^3. It is guaranteed that all inputs are correct and give the opportunity for such a tournament.

Output data

In a single line separated by a space two numbers - the number of won one of the teams meet in the tournament and the number of meetings recognized a draw.

Examples

Input example #1
100 8 11
Output example #1
12 16
Source Stage II Ukrainian School Olympiad 2011-2012, Berdichev