
90  The 7th Zhejiang Provincial Collegiate Programming Contest  H
There is a very simple and interesting oneperson game. You have 3 dice, namely Die1, Die2 and Die3. Die1 has K_{1} faces. Die2 has K_{2} faces. Die3 has K_{3} faces. All the dice are fair dice, so the probability of rolling each value, 1 to K_{1}, K_{2}, K_{3} is exactly 1 / K_{1}, 1 / K_{2} and 1 / K_{3}. You have a counter, and the game is played as follow:
Calculate the expectation of the number of times that you cast dice before the end of the game. Input There are multiple test cases. The first line of input is an integer T (0 < T <= 300) indicating the number of test cases. Then T test cases follow. Each test case is a line contains 7 nonnegative integers n, K_{1}, K_{2}, K_{3}, a, b, c (0 <= n <= 500, 1 < K_{1}, K_{2}, K_{3} <= 6, 1 <= a <= K_{1}, 1 <= b <= K_{2}, 1 <= c <= K_{3}). Output For each test case, output the answer in a single line. A relative error of 1e8 will be accepted. Sample Input 2 0 2 2 2 1 1 1 0 6 6 6 1 1 1 Sample Output 1.142857142857143 1.004651162790698 Author: CAO, Peng Source: The 7th Zhejiang Provincial Collegiate Programming Contest 