Jackpots#11316
The rules of the final round of King's Lottery in Byteland are simple:
Initially, the bag contains red balls, green balls, and blue balls. The player starts drawing balls from the opaque bag.
After a ball is drawn, it is not returned to the bag.
The player continues drawing balls until he has collected all red balls, or all green balls, or all blue balls.
The player wins the Gold Jackpot if he collects all red balls, the Silver Jackpot if he collects all green balls, and the Bronze Jackpot otherwise.
Given , and , calculate the probabilities of winning each jackpot.
Сontains three integers , and c~(1 \le a, b, c \le 1000).
Print three irreducible fractions p_G, p_S, and p_B representing the probabilities of winning the Gold Jackpot, the Silver Jackpot, and the Bronze Jackpot, respectively. Each fraction must be printed in the form .
Example 1
Example 2