Problem Description

Little A has come to college and majored in Computer and Science.

Today he has learned bit-operations in Algorithm Lessons, and he got a problem as homework.

Here is the problem:

You are giving n non-negative integers $a_1,a_2,\cdots ,a_n$, and some queries.

A query only contains a positive integer p, which means you
are asked to answer the result of bit-operations (and, or, xor) of all the integers except $a_p$.

Input

There are no more than 15 test cases.

Each test case begins with two positive integers n and p
in a line, indicate the number of positive integers and the number of queries.

$2 \leq n,q \leq 10^5$

Then n non-negative integers $a_1,a_2,\cdots,a_n$ follows in a line, $0 \leq a_i \leq 10^9$ for each i in range[1,n].

After that there are q positive integers $p_1,p_2,\cdots,p_q$in q lines, $1 \leq p_i \leq n$ for each i in range[1,q].

Output

For each query p, output three non-negative integers indicates the result of bit-operations(and, or, xor) of all non-negative integers except $a_p$ in a line.

3 3
1 1 1
1
2
3

1 1 0
1 1 0
1 1 0