No submission language available for this problem.

Description

Input

The first line contains a single integer $n$ $(1 \le n \le 2 \cdot 10^{5})$  — the size of arrays $a$ and $b$.

The second line contains $n$ integers $a_1, a_2, ..., a_n$ $(1 \le a_i \le 10^6)$.

The third line contains $n$ integers $b_1, b_2, ..., b_n$ $(1 \le b_i \le 10^6$ for $i \neq 1$; $b_1 = -1$, representing that the value of $b_1$ is unknown$)$.

The fourth line contains a single integer $q$ $(1 \le q \le 2 \cdot 10^{5})$  — the number of questions.

Each of the following $q$ lines contains a single integer $x_i$ $(1 \le x_i \le 10^6)$  — representing the $i$-th question.

Output

Output $q$ integers  — the answers to each of his $q$ questions.

Samples

2
3 7
-1 5
3
1
4
3

2
4
2

6
2 5 4 1 3 6
-1 4 6 2 3 5
3
1
8
4

10
29
9

Note

Consider the first test case.

• $b_1 = 1$: We need to convert $[3, 7] \rightarrow [1, 5]$. We can perform the following operations:

  $[3, 7]$ $\xrightarrow[\text{decrease}]{\text{i = 1}}$ $[2, 6]$ $\xrightarrow[\text{decrease}]{\text{i = 1}}$ $[1, 5]$

  Hence the answer is $2$.

• $b_1 = 4$: We need to convert $[3, 7] \rightarrow [4, 5]$. We can perform the following operations:

  $[3, 7]$ $\xrightarrow[\text{decrease}]{\text{i = 2}}$ $[3, 6]$ $\xrightarrow[\text{decrease}]{\text{i = 2}}$ $[3, 5]$ $\xrightarrow[\text{increase}]{\text{i = 1}}$ $[4, 6]$ $\xrightarrow[\text{decrease}]{\text{i = 2}}$ $[4, 5]$

  Hence the answer is $4$.

• $b_1 = 3$: We need to convert $[3, 7] \rightarrow [3, 5]$. We can perform the following operations:

  $[3, 7]$ $\xrightarrow[\text{decrease}]{\text{i = 2}}$ $[3, 6]$ $\xrightarrow[\text{decrease}]{\text{i = 2}}$ $[3, 5]$

  Hence the answer is $2$.