Codeforces Round 685 (Div. 2) |
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Finished |

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D. Circle Game

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputUtkarsh 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.

Input

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 $$$k$$$ ($$$1 \leq k \leq d$$$).

Output

For each test case, if Ashish wins the game, print "Ashish", otherwise print "Utkarsh" (without the quotes).

Example

Input

5 2 1 5 2 10 3 25 4 15441 33

Output

Utkarsh Ashish Utkarsh Utkarsh Ashish

Note

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.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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