Between attending classes, playing in rehearsals, and eating food, Capba has quite the busy university schedule. The campus consists of locations, numbered from to , with paths, numbered from to , running amongst them. Path directly connects locations and , and takes minutes to traverse in either direction. These paths are the only way to travel between locations.
Today, Capba has engagements, numbered from to . Engagement takes place at location , starting minutes after the start of the day, and lasting minutes . Yes, it's a particularly long day. The engagements are numbered in increasing order of their start times, and no two will start at the same time.
Capba leaves location (his residence) at time zero. It's possible that he won't be able to make it to everything, due to the lengths of the engagements as well as the travel times in between them. Capba decides that he's not feeling particularly dynamic today, and adopts the following strategy: Once at an engagement, he sits through it until it's over, and then he walks to the next engagement which he can make it to on time (or early). (He may also choose not to walk at all, if the next engagement's location is the same as his current location.)
Given Capba's busy schedule, determine which engagements he will end up attending.
Line : , .
Next lines: , , .
Next line: .
Next lines: , , .
All values are integers.
One per line, the numbers of the engagements which Capba will honour, in increasing order.
5 5 1 2 10 5 1 2 3 5 6 2 4 3 4 5 4 6 1 5 5 5 12 1 2 20 100 3 77 100 1 129 2 4 136 10
1 2 3 5
Capba starts at location , and is there from time until time .
He then walks to location , arriving early for engagement . He remains there until time .
He then walks to location , via location , arriving just on time for engagement , which lasts until time .
Meanwhile, he must skip engagement .
Following paths through locations and , Capba can barely make it on time to engagement , which runs from time to time .
However, it takes at least minutes to reach location from location , so he cannot make it to engagement on time and must skip it.