Sereja and Game 2

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Read problems statements in Mandarin Chinese and Russian.
Sereja is playing a game called Winner Eats Sandwich with his friends. There are N persons in total, including Sereja. Sereja is allotted the number 1, while his friends are allotted numbers from 2 to N. A set of this game consists of M parts. Probability that a player numbered i wins part j of any set is p[i][j]. Sereja and his friends play all the M parts of the first set. If someone wins all the parts, he is declared the winner of the match. Otherwise, another set of the game is played. A match of the game continues until someone wins a set. The winner of the set is then declared the winner of the game, and gets to eat the sandwich.
Now Sereja is interested in the probability with which he can win the match in no more than 10^(10^(10^(10^(10^10)))) sets. This is because the sandwich gets cold by the end of these many sets, and Sereja hates cold sandwiches.
Input
First line contains the number of test cases, T. The description of the T tests follows. First line of each test case contains two space separated integers N, M. Each of the next N lines contain M spaceseparated numbers, with the j^{th} number of the i^{th} line denoting p[i][j]. All numbers will be given with not more than 4 digits after the decimal point.
Output
For each test case, output the probability Sereja is interested in, with 6 digits after the decimal point.
Constraints
 1 ≤ T ≤ 3
 1 ≤ N ≤ 13
 1 ≤ M ≤ 10000
 it is guaranteed that for each j, the sum p[1][j] + p[2][j] + ... + p[N][j] is 1
Subtask 1 (10 points)
 1 ≤ N, M ≤ 4
Subtask 2 (90 points)
 Original constrains
Example
Input: 2 2 2 1.0000 1.0000 0.0000 0.0000 2 3 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 Output: 1.000000 0.500000
Author:  sereja 
Tester:  mugurelionut 
Editorial  http://discuss.codechef.com/problems/SEAGM2 
Tags  easymedium, july15, maths, probability, sereja 
Date Added:  10092014 
Time Limit:  3 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.5, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, CLOJ, FS 
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