XOR Sum

You start with an empty list of numbers and process $Q$ instructions in the order they are given.

• insert N: put $N$ into the list. The same number can arrive more than once.
• print: take the $K$ largest numbers in the list and output their XOR sum. If the list holds fewer than $K$ numbers, output the XOR sum of every number in the list, and if the list is empty, output $0$.

The XOR sum of a group of numbers is the result of XOR-ing all of them together. Most languages compute the XOR of two integers with the ^ operator. Haskell uses xor.

Equal values count as separate elements. If the list is $[5, 5, 3]$ and $K = 2$, the two chosen numbers are $5$ and $5$, so the XOR sum is $0$.

XOR has a useful property: if $N \oplus M = X$, then $N = X \oplus M$ and $M = X \oplus N$.

The first line contains the number of test cases $T$ ($1 \le T \le 30$).

The first line of each test case contains $Q$ and $K$ ($1 \le Q, K \le 100\,000$). The next $Q$ lines each hold one instruction, in one of these two forms:

insert N

print

$N$ is a non-negative integer smaller than $2^{31}$.

For each print instruction, output the answer on its own line. The list starts empty again for every test case.