Migrated from Lutece 1024 Flying Chess

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Description

Ye.Dong likes playing flying chess very much, so he wants Ye.Han to play with him.

To simplify the problem, we define the rules as follows:

1. Ye.Dong and Ye.Han both have two plane chesses. All chesses are at point $0$ at the very begining. When two planes of a person both reach the destination(point $N$), he'll win the game.
2. If one of the planes of a person has not reach the destination(point $N$), the another plane of his cannot take off.
3. Two people throw a dice by turns, and the number($1$~$6$) is the steps that the taken-off plane will fly forwards.
4. The plane, which has not taken off(in other words, at the point $0$), can take off(fly from point $0$ to point $1$) only if he throws a dice and get the number $6$.
5. If a plane of person A will fly to point $x(1 < x < N)$, and there is already one plane belonging to person B, the personA's plane will reach the point x, and the personB's will return to point 0.
6. We assume that $N = 5$ and you are at the point $3$ now, then you will reach the destination(point $N$) if you get the number $2, 3, 4, 5, 6$ after throwing a dice.
7. Ye.Dong takes the first turn.

Now you know the number they'll get after throwing a dice. Your task is to find out who will win the game.

Input

The first line contains only one integer, $T$, which is the number of test cases.

For each case:

The first line contains two integers, $N$ and $M (1 \leq N, M \leq 10000)$. $N$ is the number of the destination point. They both will throw a dice for $M$ times.

The following two lines both contain $M$ integers, representing the number of dice of Ye.Dong and Ye.Han will get.

Output

For each case:

Print Ye.Dong if Ye.Dong wins; print Ye.Han if Ye.Han wins.

If no one wins after $M$ turns, print Tie.

Samples

3
5 5
6 4 6 2 2 
6 4 6 4 6
5 5
6 4 6 2 2 
6 4 6 2 2
5 2
6 1
1 1

Ye.Han
Ye.Han
Tie.

Note

For Sample $1$:

1. Ye.Dong: plane$1$ -> $1$
2. Ye.Han: plane$1$ -> $1$
3. Ye.Dong: plane$1$ -> $5$ (destination point $N$)
4. Ye.Han: plane$1$ -> $5$ (destination point $N$)
5. Ye.Dong: plane$2$ -> $1$
6. Ye.Han: plane$2$ -> $1$
7. Ye.Dong: plane$2$ -> $3$
8. Ye.Han: plane$2$ -> $5$ (destination point $N$) Ye.Han wins (There are still some numbers of dice. You can just assume that they are killing the time. = =!)

For Sample $2$:

1. Ye.Dong: plane$1$ -> $1$
2. Ye.Han: plane$1$ -> $1$
3. Ye.Dong: plane$1$ -> $5$ (destination point $N$)
4. Ye.Han: plane$1$ -> $5$ (destination point $N$)
5. Ye.Dong: plane$2$ -> $1$
6. Ye.Han: plane$2$ -> $1$
7. Ye.Dong: plane$2$ -> $3$
8. Ye.Han: plane$2$ -> $3$, and then Ye.Dong's plane$2$ will return back to point $0$
9. Ye.Dong: the number is not $6$, so the plane$2$ cannot take off
10. Ye.Han: plane$2$ -> $5$ (destination point $N$) Ye.Han wins

Resources

GuessEver