A standard physical experiment is to drop a ball to see how high it bounces. Once the "bounciness" of the ball is determined, the ratio gives a bounciness index. For example, if a ball dropped from a height of 10 feet bounces 6 feet high, the index is 0.6 and the total distance travelled by the ball is 16 feet after one bounce. If the ball continues bouncing, the distance after two bounces would be 10+6+3.6=25.6 ft. Note that the distance travelled for each bounce is the distance to the floor plus 0.6 of that distance as the ball comes back up. Write a program that takes as inputs the initial height of the ball (in feet), the index of the ball's bounciness, and the number of times the ball is allowed to continue bouncing. The program should output the total distance travelled by the ball. At some point in the process, the distance travelled by the ball after a bounce might become negligable, for example, for example, less than 0.00001 inches. If that stage is reached, terminate the process and output the total distance.
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