# Practice on Toph

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## The Perfect Collection

Given an array **A** of **N** integers, if we choose any **K** of these integers and calculate their bitwise **XOR**, what is the minimum possible result that we can get?

A bitwise **XOR** takes two bit patterns of equal length and performs the logical exclusive OR operation on each pair of corresponding bits. The result in each position is **1** if only the first bit is **1** or only the second bit is **1**, but will be **0** if both are **0** or both are **1**. In this we perform the comparison of two bits, being **1** if the two bits are different, and **0** if they are the same. For more detail, visit Wikipedia

#### Input

The first line of the input contains two integers, **N** (1 ≤ N ≤ 10^{2}) and **Q** (1 ≤ Q ≤ 10^{3}), the size of the given array and the number of queries .

The next line contains **N** space separated integers, the elements of the array **A** (1 ≤ A_{i} ≤ 10^{3}).

The next **Q** lines contain one integer each. **i**^{th} of these integers represents the value of **K** (1 ≤ K ≤ N) for the **i**^{th} query.

#### Output

For each query, print one integer in a separate line: the minimum possible bitwise **XOR** value of any **K** integers of the given array.

#### Samples

Input | Output |
---|---|

4 2 2 5 7 4 2 1 | 1 2 |

#### Explanation

For the first query, the possible choices here are: (2,5), (2,7,), (2,4), (5,7), (5,4), (7,4).
Among these, the bitwise **XOR** of (5,4) yields 1 which is the minimum of all the six possible results.

For the second query, 2 is minimum value in the given array.

#### Labib666

Labib loves to solve problems unless confronted with real life ones which he procrastinates upon with food and sitcoms. →