Note

Problem Statement

Two magical girls, Mami and Homura, were having a gunfight in a sealed room of width \(W\) meters and depth \(H\) meters.

Homura stopped time and, at the same moment, fired her last shot.
In the world of stopped time, only Homura and the bullet can move. When the bullet hits a wall, it reflects at the same angle as the angle of incidence and keeps flying forever without losing speed.

Let \((Mx, My)\) be Mami's position, \((Hx, Hy)\) be the position from which Homura fired, and \((Vx, Vy)\) be the velocity vector of the bullet when fired. When time is stopped for \(D\) seconds,
determine whether the bullet can hit Mami within \(D\) seconds.

Here, the sizes of Mami and the bullet are negligible, and Homura is never hit by the bullet.

Figure: Example of an arrangement

Input

\(Q\)
\(W_{1}\) \(H_{1}\) \(D_{1}\) \(Mx_{1}\) \(My_{1}\) \(Hx_{1}\) \(Hy_{1}\) \(Vx_{1}\) \(Vy_{1}\)
\(W_{2}\) \(H_{2}\) \(D_{2}\) \(Mx_{2}\) \(My_{2}\) \(Hx_{2}\) \(Hy_{2}\) \(Vx_{2}\) \(Vy_{2}\)
\(\ldots\)
\(W_{Q}\) \(H_{Q}\) \(D_{Q}\) \(Mx_{Q}\) \(My_{Q}\) \(Hx_{Q}\) \(Hy_{Q}\) \(Vx_{Q}\) \(Vy_{Q}\)

All inputs are given as integers.

• \(1 \leq Q \leq 10000\) denotes the number of test cases.
• The \(Q\) lines starting from the second line each give a set of \(W, H, D, Mx, My, Hx, Hy, Vx, Vy\).
• \(2\leq W, H\leq 10^9\)
• \(1 \leq D \leq 10^9\)
• \(0 < Mx, Hx < W\)
• \(0 < My, Hy < H\)
• \(-10^9 \leq Vx, Vy \leq 10^9\)
• \((Mx, My) \neq (Hx, Hy)\) is guaranteed.
• \((Vx, Vy) \neq (0, 0)\) is guaranteed.

Output

Sample

5
9 9 74 7 6 4 1 -5 2
7 11 30 5 4 5 10 13 8
15 4 17 10 3 12 3 -3 1
3 9 22 2 2 1 1 13 12
8 11 2 6 5 1 9 -2 -4

Miss
Hit
Miss
Miss
Miss

5
2 15 19 1 2 1 4 1 5
5 5 11 3 1 4 2 9 -7
13 6 68 8 2 11 2 -13 0
2 15 90 1 2 1 8 0 -7
11 4 77 9 1 10 1 -6 13

Miss
Miss
Hit
Hit
Miss