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>
// Dummy text
import java.io.*; 
import java.util.*; 
  public class Games_of_circel
  {  
    public static void main(String[] args) throws IOException 
    { 
      BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); 
      int t = Integer.parseInt(br.readLine()); 
       while (t-- > 0) 
       { 
           String line = br.readLine(); 
            String[] strs = line.trim().split("\\s+");
           int d = Integer.parseInt(strs[0]);
           int k = Integer.parseInt(strs[01]);
           int x0=0;
           int y0=0;
           int hold=0;
           for(int i=0;i<1000000;i++)
           {

               if((x0+k)*(x0+k)+y0*y0 >d*d ||(y0+k)*(y0+k)+x0*x0>d*d)
               {
                   hold=i+1;
                   break;
                }
                else
                {
               if(i%2==0)
               x0+=k;
               else
               y0+=k;
            }
        }
        String answer="";
        if(hold%2==0)
        answer="ASHISH";
        else
        answer="UTKARSH";
        System.out.println(answer);
    }
    }
}