XOR Sum

You will be given a list of q (1 ≤ q ≤ 100000) instructions.

If the instructions is to "insert n", insert n into the list of numbers (there may be duplicates).

If the instruction is to "print" - print the XOR sum of the largest k (1 ≤ k ≤ q) elements in the list (or, if the list contains less than k elements, the XOR sum of all elements in the list).

XOR sum of a list of numbers is the result of XOR-ing all of them. XOR can be applied to two integers using the built in ^ operator in most languages (or xor in Haskell (Pascal)).

Note that XOR function has some useful properties, among them that if n ^ m = x then n = x ^ m and m = x ^ n.

Input

First line contains the number t (1 ≤ t ≤ 30) of test cases. Each test case start with a line containing two integers q and k (1 ≤ q, k ≤ 100000). Following are q lines containing one instruction each.

Instructions are in either of the following two forms:

insert n

or

print

n is a non-negative integer less than 2^31.

Output

For each print statement output the XOR sum of (at most) k largest elements in the current list. Note that the list is cleared between test cases.

Examples