Imagine you have a bag, which is filled with N balls. Each ball can have the color black or white. You know that W balls in the bag are white.
If you extract a ball from the bag, the probability changes of the remaining balls.
Your job is it to output the ratio of the odds that you extracted k white balls after extracting s balls from the bag. Balls are never put back into the bag!
Example: You have 3 balls in the bag, 2 of which are white. What is the probability of having 2 white balls by extracting 2 balls?
2/3 * 1/2 = 1/3
When A is the event of getting 2 white balls: P(A) = Probability of getting 2 white balls = 2/3 * 1/2 = 1/3 P(!A) = Probability of not getting 2 white balls = 1-1/3 = 2/3
So the ratio P(A) : P(!A) is 1:2 (read 1 to 2).
The ratio 2:4 would be the same ratio, but both numbers are divisible by 2, so you need to reduce the ratio.
Input
Line 1: An Integer N for the number of balls in your bag. Line 2: An Integer W for the number of white balls in your bag. Line 3: An Integer s for the size of your sample. Line 4: An Integer k for the desired number of white balls in your sample.
Output
Line 1:A : B, the odds ratio (in lowest terms) that k white balls are in your sample of s balls
Constraints
0 ≤ N ≤ 60 0 ≤ W ≤ N 0 ≤ s ≤ N 0 ≤ k ≤ s 0 ≤ k ≤ W
