Home

Contest: Task: Related: TaskB

Score : $100$ points

Problem Statement

Takahashi and Aoki decided to jog.
Takahashi repeats the following: "walk at $B$ meters a second for $A$ seconds and take a rest for $C$ seconds."
Aoki repeats the following: "walk at $E$ meters a second for $D$ seconds and take a rest for $F$ seconds."
When $X$ seconds have passed since they simultaneously started to jog, which of Takahashi and Aoki goes ahead?

Constraints

  • $1 \leq A, B, C, D, E, F, X \leq 100$
  • All values in input are integers.

Input

Input is given from Standard Input in the following format:

$A$ $B$ $C$ $D$ $E$ $F$ $X$

Output

When $X$ seconds have passed since they simultaneously started to jog, if Takahashi goes ahead of Aoki, print Takahashi; if Aoki goes ahead of Takahashi, print Aoki; if they have advanced the same distance, print Draw.

Sample Input 1

4 3 3 6 2 5 10

Sample Output 1

Takahashi

During the first $10$ seconds after they started to jog, they move as follows.

  • Takahashi walks for $4$ seconds, takes a rest for $3$ seconds, and walks again for $3$ seconds. As a result, he advances a total of $(4 + 3) \times 3 = 21$ meters.
  • Aoki walks for $6$ seconds and takes a rest for $4$ seconds. As a result, he advances a total of $6 \times 2 = 12$ meters.

Since Takahashi goes ahead, Takahashi should be printed.

Sample Input 2

3 1 4 1 5 9 2

Sample Output 2

Aoki

Sample Input 3

1 1 1 1 1 1 1

Sample Output 3

Draw