Codeforces Round 685 (Div. 2) |
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Finished |
Utkarsh is forced to play yet another one of Ashish's games. The game progresses turn by turn and as usual, Ashish moves first.
Consider the 2D plane. There is a token which is initially at $$$(0,0)$$$. In one move a player must increase either the $$$x$$$ coordinate or the $$$y$$$ coordinate of the token by exactly $$$k$$$. In doing so, the player must ensure that the token stays within a (Euclidean) distance $$$d$$$ from $$$(0,0)$$$.
In other words, if after a move the coordinates of the token are $$$(p,q)$$$, then $$$p^2 + q^2 \leq d^2$$$ must hold.
The game ends when a player is unable to make a move. It can be shown that the game will end in a finite number of moves. If both players play optimally, determine who will win.
The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 100$$$) — the number of test cases.
The only line of each test case contains two space separated integers $$$d$$$ ($$$1 \leq d \leq 10^5$$$) and $$$k$$$ ($$$1 \leq k \leq d$$$).
For each test case, if Ashish wins the game, print "Ashish", otherwise print "Utkarsh" (without the quotes).
5 2 1 5 2 10 3 25 4 15441 33
Utkarsh Ashish Utkarsh Utkarsh Ashish
In the first test case, one possible sequence of moves can be
$$$(0, 0) \xrightarrow{\text{Ashish }} (0, 1) \xrightarrow{\text{Utkarsh }} (0, 2)$$$.
Ashish has no moves left, so Utkarsh wins.
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