This page is still under construction.

Parts of this page are still being built. What you see may change.

Ye Holy Hand Grenades!

Time limit1sMemory limit128 MB

Summary
Judge whether each rabbit survives a blast from the fixed resting place of a unit grenade in an exponential and log valley.
Level

Medium7 of 10

Topics
Geometry, Math
Solved
No attempts yet

Problem

Holy Hand Grenades have found many uses through history. King Arthur used one to dispatch the vicious rabbit that guarded the entrance to a cave. The instructions for its use are in the Book of Armaments, chapter 2, verses 9 to 21.

The Book of Armaments forgets to mention one thing. A Holy Hand Grenade only explodes once it has come to a complete stop and rests stably. As long as it rolls or wobbles, it refuses to explode. Grenades also differ in their radius of destruction RDRD. Once a grenade rests and explodes, everything at distance RDRD or less from its center is snuffed out. To settle the argument about the rabbit with big pointy teeth, the king ordered a simulation.

  • Every grenade is a circle of radius R=1R = 1, and the radius of destruction RDRD varies from grenade to grenade.
  • The terrain never changes. It is the valley formed by the two intersecting curves y=e−xy = e^{-x} and y=ln⁡xy = \ln x, lying in the plane through the rabbit, the grenade, and the center of the earth. At horizontal position xx the ground sits at height max⁡(e−x,ln⁡x)\max(e^{-x}, \ln x), the upper of the two curves. Explosions leave the terrain untouched.
  • The grenade settles as deep into the valley as it can go, which is the single position where it touches both curves at once. It always detonates from there.
  • The rabbit is given by its center of mass (xb,yb)(x_b, y_b). At the instant of detonation it may be mid-leap, on the ground, or underground.
  • A rabbit whose center of mass is strictly below the ground survives and lives to bite another day.
  • A rabbit whose distance from the grenade's center is greater than RDRD survives. At distance RDRD or less it is blown to bits.
  • A rabbit can be inside RDRD and inside the grenade body R=1R = 1 at the same time. That just means it is curled around the grenade, and being strictly inside RDRD still blows it to bits.
  • Every computation has to be accurate to 8 significant figures.

Input

The first line contains an integer, the number of holy hand grenades. Each following line describes one test run: the radius of destruction RDRD of that grenade, then the rabbit's x coordinate xbx_b and y coordinate yby_b, separated by spaces. Every value in the input is between 10−1510^{-15} and 101510^{15}.

Output

For each test run, print Bunny Bits on its own line if the grenade blows the rabbit to bits, or Bunny Biteth Knights if the rabbit lives to fight on another day.

Examples2

  1. Example 1

    Input
    2
    1.5 3.0 3.0
    5.5 3.0 3.0
    
    Expected output
    Bunny Biteth Knights
    Bunny Bits
    
  2. Example 2

    Input
    3
    1000.0 5.0 1.0
    1000.0 0.5 0.1
    1000.0 1.3097995858 0.2
    
    Expected output
    Bunny Biteth Knights
    Bunny Biteth Knights
    Bunny Biteth Knights