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 $N$ $(1\le N\le 50000)$ 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.