Jackpots
Jackpots
The rules of the final round of King's Lottery in Byteland are simple:
The player starts to draw balls from an opaque bag containing a red balls, b green balls and c blue balls initially.
After the player draws the ball, the ball is not returned into the bag.
The player continues the process until he collects all a red balls, or all b green balls, or all c blue balls.
The player wins the Gold Jackpot if he collects a red balls, Silver Jackpot if he collects b green balls, or Bronze Jackpot otherwise.
Given a, b and c, calculate the probabilities of winning each jackpot.
Input data
Contains three integers a, b and c~(1 \le a, b, c \le 1000).
Output data
Print three irreducible fractions p_G, p_S and p_B denoting the probability of winning the Gold Jackpot, the Silver Jackpot and the Bronze Jackpot, respectively. The fractions shall be printed in the form p / q.
Examples
1 1 1
1/3 1/3 1/3
1 2 3
7/12 4/15 3/20