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.*;
public class D {
    public static double dist(int x, int y) {
        return Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));
    }
    public static double left(int constant, int d) {
        return Math.sqrt(Math.pow(d, 2) - Math.pow(constant, 2));
    }
    public static void main(String[] args) {
        Scanner input = new Scanner(System.in);
        int t = input.nextInt();
        for(int i = 0; i < t; i++) {
            int d = input.nextInt();
            int k = input.nextInt();
            int x = k;
            int y = 0;
            double tempdist = dist(x, y);
            int moves = 1;
            while(tempdist <= d) {
                int leftx = (int)Math.floor(left(y, d)) - x;
                int lefty = (int)Math.floor(left(x, d)) - y;
                if(Math.floor(leftx/(double)k) % 2 != 0) {
                    x += k;
                } else if(Math.floor(lefty/(double)k) % 2 != 0) {
                    y += k;
                } else {
                    if(x < y) {
                        x += k;
                    } else if(y < x) {
                        y += k;
                    } else {
                        x += k;
                    }
                }
                moves++;
                tempdist = dist(x, y);
            }
            if(moves % 2 == 1) {
                System.out.println("Utkarsh");
            } else System.out.println("Ashish");
        }
    }
}
