Problem Statement

A rabbit and a turtle are now going to compete to see how far each can advance in $10^{100}$ turns.
At the start, the distance traveled is $0$ for both the rabbit and the turtle.
The rabbit and the turtle each advance according to the following rules.

• Rabbit: On the first turn, it advances by $A$ and sets its fatigue to $D$.
  After that, its action on each turn is determined as follows.

  • If its fatigue is greater than $0$, it does not advance, and its fatigue decreases by $R$.
  • If its fatigue is $0$ or less, it advances by $A$, and its fatigue increases by $D$.

• Turtle: It advances by $B$ every turn.

Determine which of them wins, that is, which of them has traveled the longer distance after $10^{100}$ turns.
Note that a tie is also possible.

You are given $T$ test cases; answer each of them.

Constraints

• $1 \leqq B \leqq A \leqq 10^{9}$
• $1 \leqq R \leqq D \leqq 10^{9}$
• $1 \leqq T \leqq 10^5$
• All inputs are integers.

Input

$T$
$testcase_1$
$testcase_2$
$\vdots$
$testcase_T$

Each test case is given in the following format.

$A\ B\ D\ R$

Output

For each test case, print rabbit if the rabbit wins, turtle if the turtle wins, and tie if it is a tie. The output consists of $T$ lines.
Print a newline at the end.

Sample

3
3 1 1 1
1 1 2 1
4 2 1 1

rabbit
turtle
tie