Regroup! Regroup!

The caves have been completely traversed, and Mr. Benum has been located! However, the quest is not over. Swarms of bebiliths, or spider-monsters the size of elephants, are swiftly decimating the ex-convicts! It is up to Max to command the remaining ex-convicts so that they can exterminate the bebilith army. But first, Max has to ensure that the ex-convicts will stay alive!

There are ~N~ ~(1 \le N \le 50\,000)~ bebiliths in pursuit of one of the groups of ex-convicts. Each bebilith has a speed ~B~ ~(0 \le B \le 10^9)~, a venom-spitting distance ~D~ ~(0 \le D \le 10^9)~ and a claw sharpness ~C~ ~(0 \le C \le 10^9)~ (where the bebilith with the sharpest claw has the highest value of ~C~). Meanwhile, the ex-convicts are running at a uniform speed ~S~ ~(0 \le S \le 10^9)~.

If two bebiliths have the same speed and are faster or at pace with the ex-convicts, the bebilith with the sharpest claws is more dangerous. However, if two bebiliths have the same speed but are slower than the ex-convicts, the bebilith that spits venom the farthest is more dangerous. Otherwise, if two bebiliths have different speeds, the faster one is more dangerous. Max numbers each bebilith from ~1~ to ~N~. If there is a tie between two bebiliths in terms of how dangerous they are, the one that is numbered the lowest is considered more dangerous. Help Max determine what number represents the ~i^\text{th}~ most dangerous bebilith ~Q~ ~(1 \le Q \le N)~ times!

Input Specification

First line: ~S~

Second line: ~N~

Next ~N~ lines: Three space-separated integers ~B_j~ ~D_j~ ~C_j~ on each line. Line ~j~ represents the characteristics of the ~(j-2)^\text{th}~ bebilith.

Line ~N+2~: ~Q~

Next ~Q~ lines: A single integer ~i~ on each line, indicating that the ~i^\text{th}~ most dangerous bebilith's number should be reported back to Max.

Output Specification

~Q~ lines of the ~i^\text{th}~ most dangerous bebilith's number as queried.

Sample Input

5
4
7 29 61
7 42 59
4 1 441221001
3 7 9996999
4
1
2
3
4

Sample Output

1
2
3
4

Explanation

Bebiliths ~1~ and ~2~ have the same speed, and both are the fastest. Their speed is greater than Max's speed. Bebilith ~1~ has sharper claws, so it is the most dangerous, while bebilith ~2~ is the ~2^\text{nd}~ most dangerous. Bebilith ~3~ is faster than bebilith ~4~, so they are the ~3^\text{rd}~ and ~4^\text{th}~ most dangerous, respectively.