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| What is the Probability? | |
| Probability has always been an integrated part of computer algorithms. | |
| Where the deterministic | |
| algorithms have failed to solve a problem in short time, probabilistic algorithms have come to the | |
| rescue. | |
| In this problem we are not dealing with any probabilistic algorithm. | |
| We will just try to | |
| determine the winning probability of a certain player. | |
| A game is played by throwing a dice like thing (it should not be assumed that it has six sides like | |
| an ordinary dice). If a certain event occurs when a player throws the dice (such as getting a 3, getting | |
| green side on top or whatever) he is declared the winner. There can be N such player. So the first | |
| player will throw the dice, then the second and at last the N-th player and again the first player and | |
| so on. When a player gets the desired event he or she is declared winner and playing stops. You will | |
| have to determine the winning probability of one (The I-th) of these players. | |
| Input | |
| Input will contain an integer S (S ≤1000) at first, which indicates how many sets of inputs are there. | |
| The next S lines will contain S sets of inputs. Each line contain an integer N (N ≤1000) which denotes | |
| the number players, a floating point number p which indicates the probability of the happening of a | |
| successful event in a single throw (If success means getting 3 then p is the probability of getting 3 in | |
| a single throw. For a normal dice the probability of getting 3 is 1/6), and I (I ≤N) the serial of the | |
| player whose winning probability is to be determined (Serial no varies from 1 to N). You can assume | |
| that no invalid probability (p) value will be given as input. | |
| Output | |
| For each set of input, output in a single line the probability of the I-th player to win. The output | |
| floating point number will always have four digits after the decimal point as shown in the sample | |
| output. | |
| Sample Input | |
| 2 | |
| 2 0.166666 1 | |
| 2 0.166666 2 | |
| Sample Output | |
| 0.5455 | |
| 0.4545 |