CF311B Cats Transport

Zxr960115 is owner of a large farm. He feeds $ m $ cute cats and employs $ p $ feeders. There's a straight road across the farm and $ n $ hills along the road, numbered from 1 to $ n $ from left to right. The distance between hill $ i $ and $ (i-1) $ is $ d_{i} $ meters. The feeders live in hill 1. One day, the cats went out to play. Cat $ i $ went on a trip to hill $ h_{i} $ , finished its trip at time $ t_{i} $ , and then waited at hill $ h_{i} $ for a feeder. The feeders must take all the cats. Each feeder goes straightly from hill 1 to $ n $ without waiting at a hill and takes all the waiting cats at each hill away. Feeders walk at a speed of 1 meter per unit time and are strong enough to take as many cats as they want. For example, suppose we have two hills $ (d_{2}=1) $ and one cat that finished its trip at time 3 at hill 2 $ (h_{1}=2) $ . Then if the feeder leaves hill 1 at time 2 or at time 3, he can take this cat, but if he leaves hill 1 at time 1 he can't take it. If the feeder leaves hill 1 at time 2, the cat waits him for 0 time units, if the feeder leaves hill 1 at time 3, the cat waits him for 1 time units. Your task is to schedule the time leaving from hill 1 for each feeder so that the sum of the waiting time of all cats is minimized.

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