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 sys,functools,collections,bisect,math,heapq
input = sys.stdin.readline
#print = sys.stdout.write 
sys.setrecursionlimit(200000000)
@functools.lru_cache(None)
def fun(x,y,d):
    if x < y:
        dis = (x+k)**2 + y**2
        if dis <= d:
            if not(fun(x+k,y,d)):
                return True
            dis = x**2 + (y+k)**2
            if dis <= d:
                if not(fun(x,y+k,d)):
                    return True
        
    else:
        dis = x**2 + (y+k)**2
        if dis <= d:
            if not(fun(x,y+k,d)):
                return True
            dis = (x+k)**2 + y**2
            if dis <= d:
                if not(fun(x+k,y,d)):
                    return True
    return False
t = int(input())
for _ in range(t):
    d,k = map(int,input().strip().split())
    d *= d
    if fun(0,0,d):
        print('Ashish')
    else:
        print('Utkarsh')
    