Read problems statements in Mandarin Chinese  and Russian. 

In a far away dystopian world, the measure of the quality of a person’s life is the numbers of likes he gets for an article about their life. For a person to stay alive, he has to acquire at least L number of likes before D days pass.

People in this world employ various techniques to increase the number of likes. One of the famous ones is to dis-like and re-like their own article once per day. On doing so you can assume that the number of likes for the post increase by a constant factor C.

So if one starts with S likes on Day-1, he would have D2 = S + C * S likes on Day-2,    D3 = D2 + D2 * C on Day-3 etc. You are to answer if the person would survive at the end of Day-D or not.

Input

First line contains a single positive integer T denoting the number of test cases. The following T lines represent a test case each. Each test case contains 4 space-separated integers L, D, S and C.

Output

For each test case, print a single line containing “ALIVE AND KICKING” if the person would live, otherwise print, “DEAD AND ROTTING”.

Constraints

1 ≤ T ≤ 1000
1 ≤ L ≤ 1000000000
1 ≤ D ≤ 1000000000
1 ≤ S ≤ 1000000000
1 ≤ C ≤ 1000000000

----- Sample Input 1 ------ 
2
5 1 5 1
10 2 2 2
----- Sample Output 1 ------ 
ALIVE AND KICKING
DEAD AND ROTTING

----- explanation 1 ------ 
In the first case by the end of Day-1 we would be having S that is 5 number of likes, as it is ? L, the answer is ALIVE AND KICKING.
In the second case, D2 =S + C*S, therefore D2 = 2 + 2 * 2 = 6, as 6 is less than 10, the answer is DEAD AND ROTTING.