Little K has n dice which have x sides, each with faces numbered 1,2,...,x-1,x. Big S has m dice which have y sides, each with faces numbered 1,2,...y-1,y.

Now they want to play a game. They roll their dice and compare total scores,the highest scores wins.What is the probability that little K can win ?

The first line contains one integer T, indicates the total test cases. Each test case contains four integer n, x, m, y.1<=n,m<=100,1<=x,y<=10,T<=20

Print a number with exactly 7 decimal places.