Granny can upend the cream can, thus pouring its contents on the ground. But due to surface tension and the shape of the can a small amount of the content remains, even after the can is upended. Granny has a barrel full of rain water that she can use to rinse the can several times. Each rinse involves pouring some amount of water (perhaps none) into the cream can, mixing it thoroughly with the existing contents, and pouring it out. After each rinse an amount of liquid remains, some fraction of which is whiskey and the rest water.
Mr. Ness' visit is imminent, affording Granny the time to do at most k rinses. You are to determine a rinsing strategy that Granny should employ to minimize the amount of residual whiskey in the cream can after the last rinse.
Standard input consists of several test cases. Each test case is represented by a line with five numbers:
Note that the total amount of water used in all rinses must not exceed Vb. The total amount of liquid in the cream can cannot exceed Vc at any time. Assume that whiskey and water mix perfectly and that their volumes are additive; that is, x units of whiskey and y units of water combine to form x+y units of liquid.
2 15.0 25.0 1.0 50.0 0
2 0.00 15.00