(K, N)-Knight

On an infinitely large chessboard you are given two squares $(x_1, y_1)$ and $(x_2, y_2)$. Write a program that decides whether a $(K, N)$-knight can travel from $(x_1, y_1)$ to $(x_2, y_2)$.

A $(K, N)$-knight moves much like an ordinary knight. In a single move it can jump to a square that is $K$ columns and $N$ rows away, or $N$ columns and $K$ rows away. In other words, from $(x, y)$ it moves to one of $(x \pm K, y \pm N)$ or $(x \pm N, y \pm K)$. The ordinary chess knight is a $(2, 1)$-knight (equivalently a $(1, 2)$-knight).

The first line contains the number of test cases $T$ ($1 \le T \le 20{,}000$). Each test case is a single line with six integers $K$, $N$, $x_1$, $y_1$, $x_2$, $y_2$ separated by spaces. ($0 \le K, N \le 10^9$, $K + N > 0$, $-10^9 \le x_1, y_1, x_2, y_2 \le 10^9$)

For each test case, print TAK if the $(K, N)$-knight can move from $(x_1, y_1)$ to $(x_2, y_2)$, or NIE otherwise. Print one answer per line.