In an ACM regional contest held in Shiraz University, two problems A and B are given. The problems have positive weights and the final score of a team is computed as the weighted sum of the numbers of solved test-cases for the two problems. Only the best k teams will advance to the world finals where the integer 1 ≤ k ≤ n − 1 is randomly chosen from a uniform distribution by the ACM international headquarters and announced only after the list of the team scores is submitted. The weights of the problems are not known to the participating teams prior to the end of the contest following which the site manager will work out the weights so as to maximize the expected number of qualifying teams from Shiraz University over the unknown value of k. Given the number of solved test-cases for each problem by each team, compute the maximum possible value of the expected number of Shiraz University teams which will compete in the final world competition. Input On the first line of input is given an integer T of the number of test-cases. The first line of each test-case contains two integers 1 < n ≤ 10,000, the total number of teams, followed by m < 20, the number of teams from Shiraz University. For the next n lines, the i-th line has the number of test-cases (not greater than 10,000) solved by the i-th team for problems A and B in the same order. The first m lines are associated with the teams from Shiraz University. Output For each test-case print on a new line the maximum possible value of the expected number of teams from Shiraz University that will have berths in the world finals. All values have to be printed in exactly 4 decimal places. Sample Input 5 22 12 21 20 12 21 21 12 21 12 22 42 43 12 34 21
2/2 Sample Output 1.0000 0.0000 1.0000 0.0000 1.0000