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 interview
        {
            public static void main(String []args)
            {
               Scanner sc=new Scanner(System.in);
               int t=sc.nextInt();
               for(;t>0;t--)
               {
                   int d=sc.nextInt();
                   int k=sc.nextInt();
                   int s=0;
                   int c=0;
                   int i=0,j=0;
                   while(s<d*d)
                   {
                       c++;
                       if((i+k)*(i+k)+j*j>d*d &&(j+k)*(j+k)+i*i>d*d)
                       {
                           if(c%2==1)
                            System.out.println("Utkarsh");
                            else
                            System.out.println("Ashish");
                        break;
                }
               int x=(int)Math.sqrt(d*d-j*j);
               int y=(int)Math.sqrt(d*d-i*i);
               if((x-i)/k%2==1)
               {
                   i=i+k;
               }
               else
               {
                   j=j+k;
                }
            }
       }
    }
}
