The In-XOR-able Task

You are given three integers $N$, $K$ and $X$. Is it possible to find a sequence of non-negative integers $A_1, A_2, \ldots, A_N$ such that the number of pairs of indices $(i, j)$ ($1 \le i \le j \le N$) satisfying $A_i \oplus A_j = X$ is equal to $K$? Here, $\oplus$ is the bitwise XOR operator. ### Input - The first line of the input contains a single integer $T$ denoting the number of test c