Given an NxN chessboard and a Knight at position (x,y). The Knight has to take exactly K steps, where at each step it chooses any of the 8 directions uniformly at random. What is the probability that the Knight remains in the chessboard after taking K steps, with the condition that it can’t enter the board again once it leaves it.
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. The first line of each test case contains four integers N, X, Y and K. Where N * N is the size of the board and (X, Y) denotes the starting position of the chess piece.
Output the probability that the knight remains on the board. Print the answer exactly upto 6 decimal places for each testcase in a new line.
1<= T <=100
1<= N, K, X, Y <=100
8 0 0 3