Processing math: 100%

Problem D. Decisive throw

Author:Антон Карабанов   Time limit:1 sec
Input file:Standard input   Memory limit:512 Mb
Output file:Standard output  

Statement

Timofey and his friends became interested in tabletop role-playing games. They spend all their pocket money on character figures, dungeon maps, beautiful dice and, of course, interesting games. Today a group of friends gathered for the first time for a new game "Olympus". After four hours, they reached the high point of the game — the outcome of the game depends on Timothy's final move.

Timofey must throw n ordinary six-sided dice with numbers from 1 to 6. If at least m of them land successfully, the team of friends wins. A dice falls successfully if the number on the upper face is at least a. For example, with a=5, n=3 and m=2 Timofey must roll three dice in order to win so that at least two of them have the numbers 5 or 6.

Your program must output the probability of friends' victory in the form of an irreducible fraction.

Input format

The only line of input contains three integers: a, n и m.

Output format

Output two integers — nominator and denominator of irreducible fraction representing the probability of victory.

Constraints

1a6

1mn15

Notes on samples

In the first sample there are 36 different outcomes of throwing two dice, 27 of them are successful — the number on at least one of the dice if greater or equal than four. Therefore, probability of success is 27/36 or, after the reduction, 3/4.

Sample tests

No. Standard input Standard output
1
4 2 1
3 4
2
5 3 2
7 27

0.064s 0.008s 15