You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Bodya and Sasha found a permutation $$$p_1,\dots,p_n$$$ and an array $$$a_1,\dots,a_n$$$. They decided to play a well-known "Permutation game".

A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

Both of them chose a starting position in the permutation.

The game lasts $$$k$$$ turns. The players make moves simultaneously. On each turn, two things happen to each player:

- If the current position of the player is $$$x$$$, his score increases by $$$a_x$$$.
- Then the player either stays at his current position $$$x$$$ or moves from $$$x$$$ to $$$p_x$$$.

Knowing Bodya's starting position $$$P_B$$$ and Sasha's starting position $$$P_S$$$, determine who wins the game if both players are trying to win.

## Input Format
The first line contains a single integer $$$t$$$ ($$$1\le t\le 10^4$$$) — the number of testcases.

The first line of each testcase contains integers $$$n$$$, $$$k$$$, $$$P_B$$$, $$$P_S$$$ ($$$1\le P_B,P_S\le n\le 2\cdot 10^5$$$, $$$1\le k\le 10^9$$$) — length of the permutation, duration of the game, starting positions respectively.

The next line contains $$$n$$$ integers $$$p_1,\dots,p_n$$$ ($$$1 \le p_i \le n$$$) — elements of the permutation $$$p$$$.

The next line contains $$$n$$$ integers $$$a_1,\dots,a_n$$$ ($$$1\le a_i\le 10^9$$$) — elements of array $$$a$$$.

It is guaranteed that the sum of values of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

## Output Format
For each testcase output:

- "Bodya" if Bodya wins the game.
- "Sasha" if Sasha wins the game.
- "Draw" if the players have the same score.

## Examples
```input
10
4 2 3 2
4 1 2 3
7 2 5 6
10 8 2 10
3 1 4 5 2 7 8 10 6 9
5 10 5 1 3 7 10 15 4 3
2 1000000000 1 2
1 2
4 4
8 10 4 1
5 1 4 3 2 8 6 7
1 1 2 1 2 100 101 102
5 1 2 5
1 2 4 5 3
4 6 9 4 2
4 2 3 1
4 1 3 2
6 8 5 3
6 9 5 4
6 1 3 5 2 4
6 9 8 9 5 10
4 8 4 2
2 3 4 1
5 2 8 7
4 2 3 1
4 1 3 2
6 8 5 3
2 1000000000 1 2
1 2
1000000000 2
```
```output
Bodya
Sasha
Draw
Draw
Bodya
Sasha
Sasha
Sasha
Sasha
Bodya
```

## Note
Below you can find the explanation for the first testcase, where the game consists of $$$k=2$$$ turns.

TurnBodya's positionBodya's scoreBodya's moveSasha's positionSasha's scoreSasha's movefirst$$$3$$$$$$0 + a_3 = 0 + 5 = 5$$$stays on the same position$$$2$$$$$$0 + a_2 = 0 + 2 = 2$$$moves to $$$p_2=1$$$second$$$3$$$$$$5 + a_3 = 5 + 5 = 10$$$stays on the same position$$$1$$$$$$2 + a_1 = 2 + 7 = 9$$$stays on the same positionfinal results$$$3$$$$$$10$$$$$$1$$$$$$9$$$

As we may see, Bodya's score is greater, so he wins the game. It can be shown that Bodya always can win this game.

Now solve the problem and return the code.