HazelFan wants to build a rooted tree. The tree has n nodes labeled 0 to n−1, and the father of the node labeled i is the node labeled ⌊i−1k⌋. HazelFan wonders the size of every subtree, and you just need to tell him the XOR value of these answers.
Input
The first line contains a positive integer T(1≤T≤5), denoting the number of test cases. For each test case: A single line contains two positive integers n,k(1≤n,k≤1018).
Output
For each test case:
A single line contains a nonnegative integer, denoting the answer.