CF1451D.Circle Game

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.

乌塔卡什被迫再次参加阿西什设计的某个游戏。游戏轮流进行，且照例由阿西什先手。

考虑二维平面。初始时，一个标记位于点 $(0,0)$。在一次操作中，玩家必须将标记的 $x$ 坐标或 $y$ 坐标恰好增加 $k$。在此过程中，玩家必须确保标记始终位于以 $(0,0)$ 为圆心、欧几里得距离不超过 $d$ 的范围内。

换言之，若某次操作后标记坐标为 $(p,q)$，则必须满足 $p^2 + q^2 \leq d^2$。

当一名玩家无法进行任何合法操作时，游戏结束。可以证明，游戏必将在有限步内结束。若双方均采取最优策略，请判断谁将获胜。

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

第一行包含一个整数 $t$（$1 \leq t \leq 100$）—— 测试用例的数量。

每个测试用例仅有一行，包含两个以空格分隔的整数 $d$（$1 \leq d \leq 10^5$）和 $k$（$1 \leq k \leq d$）。

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

对于每个测试用例，如果阿西什赢得游戏，则输出 “Ashish”，否则输出 “Utkarsh”（不带引号）。

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.

在第一个测试用例中，一种可能的移动序列为：

$(0, 0) \xrightarrow{\text{阿希什 }} (0, 1) \xrightarrow{\text{乌特卡尔什 }} (0, 2)$。

阿希什已无合法移动可走，因此乌特卡尔什获胜。