Time Limit: 2 Seconds
Memory Limit: 65536 KB
In 2100, ACM chocolate will be one of the favorite foods in the world.
"Green, orange, brown, red��", colorful sugar-coated shell maybe is
the most attractive feature of ACM chocolate. How many colors have you ever
seen? Nowadays, it's said that the ACM chooses from a palette of twenty-four
colors to paint their delicious candy bits.
One day, Sandy played a game on a big package of ACM chocolates which contains
five colors (green, orange, brown, red and yellow). Each time he took one chocolate
from the package and placed it on the table. If there were two chocolates of
the same color on the table, he ate both of them. He found a quite interesting
thing that in most of the time there were always 2 or 3 chocolates on the table.
Now, here comes the problem, if there are C colors of ACM chocolates in the
package (colors are distributed evenly), after N chocolates are taken from the
package, what's the probability that there is exactly M chocolates on the table?
Would you please write a program to figure it out?
The input file for this problem contains several test cases, one per line.
For each case, there are three non-negative integers: C (C <= 100), N and
M (N, M <= 1000000).
The input is terminated by a line containing a single zero.
The output should be one real number per line, shows the probability for each
case, round to three decimal places.
5 100 2
Source: Asia 2002, Beijing (Mainland China)