Problem K
Investigating Frog Behaviour on Lily Pad Patterns

A frog in a pond.

To confirm her hypotheses about the frogs’ movement pattern, Ina set up a large number of lily pads in a pool in her laboratory, arranged in a straight line. Since the frogs were attracted to light, she was able to simplify the test setup further by placing a bright light at one end of that line. This way, the frogs would always jump in one direction (towards the light).

Of course, Ina could now place some frogs on the lily pads and sit there all day watching the frogs jump around. But as the frogs move so rarely, it would take ages to gather a sufficient amount of data.

She therefore attached to each frog a tiny device that could log all jumps of that frog. This way, she could put the frogs on the lily pads, leave them alone for a few hours and come back later to collect the data. Unfortunately, the devices had to be so tiny that there was no space for a position tracking system; instead, the devices could only record the times of the jumps.

But if the movement pattern of the frogs is as restricted as Ina thinks, surely the individual movements of the frog can be reconstructed only from the initial positions and the recorded jump time stamps?

Input

The input consists of:

• One line with an integer $n$ ($1\leq n \leq 2\cdot 10^5$), the number of frogs.

• One line with $n$ integers $x_1,\dots , x_n$ ($1\leq x_i \leq 10^6$), the number of the lily pad on which the $i$th frog initially sits. The lily pads are numbered consecutively, starting at $1$. It is guaranteed that the initial positions are strictly increasing, i.e. $x_1 < x_2 < \dots < x_n$.

• One line with an integer $q$ ($1\leq q \leq 2\cdot 10^5$), the number of jumps recorded.

• $q$ lines, each containing an integer $i$ ($1\leq i\leq n$), indicating that the $i$th frog jumped. The jumps are given in chronological order and you may assume that a jumping frog lands before the next jump begins. The frogs always jump to the nearest empty lily pad with a larger number, and you may assume that such a lily pad always exists.

Output

For each jump, output the number of the lily pad the frog lands on.

Notes

Figure 1: Illustration of the first sample case. The lily pads are numbered from left to right, starting at $1$.

5
1 2 3 5 7
3
1
2
4

4
6
8

5
1 2 3 5 7
4
1
1
1
1

4
6
8
9