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.Scanner;

public class Ashish {
    private static int x = 0;
    private static int y = 0;

    public static void main(String[] args) {
        int count, ashish, utkarsh, k, b;
        Scanner scanner = new Scanner(System.in);

        ashish = 0;
        utkarsh = 0;
        count = 0;
        b = scanner.nextInt();
        k = scanner.nextInt();

        while (true) {
            if (count % 2 == 0) {
                if (!isValidMove(k, b)) {
                    break;
                }
                ashish++;
            } else {
                if (!isValidMove(k, b)) {
                    break;
                }
                utkarsh++;
            }
            count++;
        }

        if (ashish > utkarsh) {
            System.out.println("ashish");
        } else {
            System.out.println("utkarsh");
        }
    }

    private static boolean isValidMove(int k, int d) {
        if (Math.pow((x + k), 2) + Math.pow(y, 2) <= Math.pow(d, 2)) {
            x += k;
        } else if (Math.pow((y + k), 2) + Math.pow(x, 2) <= Math.pow(d, 2)) {
            y += k;
        } else {
            return false;
        }
        return true;
    }
}
