## Queries with Fixed Length

Consider an -integer sequence, . We perform a query on by using an integer, , to calculate the result of the following expression:

In other words, if we let , then you need to calculate .

Given and queries (each query consists of an integer, ), print the result of each query on a new line.

**Input Format**

The first line consists of two space-separated integers describing the respective values of and .

The second line consists of space-separated integers describing the respective values of .

Each of the subsequent lines contains a single integer denoting the value of for that query.

**Constraints**

**Output Format**

For each query, print an integer denoting the query's answer on a new line. After completing all the queries, you should have printed lines.

**Sample Input 0**

```
5 5
33 11 44 11 55
1
2
3
4
5
```

**Sample Output 0**

```
11
33
44
44
55
```

**Explanation 0**

For , the answer is

For , the answer is

For , the answer is

For , the answer is

For , the answer is

**Sample Input 1**

```
5 5
1 2 3 4 5
1
2
3
4
5
```

**Sample Output 1**

```
1
2
3
4
5
```

**Explanation 1**

For each query, the "prefix" has the least maximum value among the consecutive subsequences of the same size.