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 ≤ 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 ≤ t ≤ 100) — the number of test cases.

The only line of each test case contains two space separated integers d (1 ≤ d ≤ 10^5) and k (1 ≤ k ≤ 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{Ashish } (0, 1) \xrightarrow{Utkarsh } (0, 2).

Ashish has no moves left, so Utkarsh wins.

<image>
import java.util.*;
import java.util.ArrayList;
public class Main {
    public static boolean is_within(long x, long y, long dsq, long k)
    {
        return dsq - k * k * x * x - k * k * y * y >= 0;
    }
    public static void main(String args[])
    {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        for(int cases = 0; cases < t; cases++)
        {
            int d = sc.nextInt();
            long dsq = ((long) d) * d;
            int k = sc.nextInt();
            int cur = 0;
            while(is_within(cur + 1, cur + 1, dsq, k))
                cur++;
            if(is_within(cur + 1, cur, dsq, k))
                System.out.println("Ashish");
            else
                System.out.println("Utkarsh");
        }
    }
}
//Read Editorial
// Let 𝑧 be the maximum integer such that the point (𝑘𝑧,𝑘𝑧) is within the circle. If the point (𝑘𝑧,𝑘(𝑧+1)) is also within the circle, player 1 wins. Otherwise player 2 wins.

// Solution:

// Regardless of what move player 1 makes, player 2 can force the token to be at some point on the line 𝑥=𝑦 at the end of his turn (if player 1 moves up, player 2 can move right and vice versa).

// Case 1: (𝑘𝑧,𝑘(𝑧+1)) lies outside the circle

// Player 2 can guarantee his victory in this fashion as player 1 will not have any moves left after reaching the point (𝑘𝑧,𝑘𝑧). Player 2 wins.

// Case 2: (𝑘𝑧,𝑘(𝑧+1)) lies within the circle

// After player 1 makes his first move, player 2 finds himself in the same situation as player 1 did in the previous case. That is, player 1 can ensure that they reach either (𝑘𝑧,𝑘(𝑧+1)) or (𝑘(𝑧+1),𝑘𝑧) in the same way. Points (𝑘(𝑧+1),𝑘(𝑧+1)) and (𝑘𝑧,𝑘(𝑧+2)) do not lie within the circle as by definition

// 𝑑2<𝑘2(𝑧+1)2+𝑘2(𝑧+1)2<𝑘2𝑧2+𝑘2(𝑧+2)2.
// Thus player 2 will not have any moves left and player 1 wins.