Description: 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. 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.