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

1 ≤ a ≤ 6

1 ≤ m ≤ n ≤ 15

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

0.288s 0.038s 15