Given an array $A$ of $n$ integers. Your task is to answer $q$ queries. Each query consists of a number $x$, requiring you to find the length of the shortest contiguous subarray $S$ of $A$ such that all values in ${1, 2, \dots, x}$ appear at least once in $S$.
### Input
- The first line contains two integers $n, q$.
- The second line contains $n$ integers $A_i$.
- The next $q$ lines each contain one integer $x$, representing a query.
### Output
- For each query, print the length of the shortest subarray that satisfies the condition. Print $-1$ if no such subarray exists.
### Constraints
- $1 \le n, q \le 2 \times 10^5$.
- $1 \le A_i \le 10^9$.
- $1 \le x \le 10^9$.
### Examples
Input:
```
5 3
1 1 2 4 3
5
4
3
```
Output:
```
-1
4
4
```
