MATGAME - Matrix Game

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Two players A and B play the following game.
1) First, a matrix M of size N*M is chosen, and filled with non-zero numbers.
2) Player A starts the game and the players play alternately.
3) In his turn, a player chooses any row which has atleast one non zero nuumber in it. In this row, the leftmost non zero number is chosen. Let this number be K. The player subtracts any number between 1 and K inclusive from it.
4) The game ends when all the numbers in the matrix M are 0.
5) The player who plays last wins the game.
Given N,M and the initial matrix, determine who wins the game. Assume that both players play optimally.


The first line contains the number of test cases T.
Each test case consists of 2 numbers N and M. There follow N lines each having M integers. The jth number on the ith line is the number M[i][j]. There is a blank line between consecutive test cases.


Output T lines, one for each case. Output "FIRST" if player A wins, else output "SECOND".


Sample Input :
2 2
1 1
1 1
1 3
2 1 1
2 2
3 2
3 2
Sample Output:


T <= 1000
1 <= N,M <= 50
The initial matrix values are between 1 and 50 inclusive.

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Md. Najim Ahmed: 2016-03-19 09:16:53

i dont know much game theory but man... i had fun solving it :v and that even in one attempt ...
nice problem :)
Thumbs Up :D

jkelava6: 2015-06-29 13:21:27

: : still coding -_- :: first player will take 2 in his first move. THEN they both take one. First player wins!

: : still coding -_- :: 2015-03-09 08:54:49

in second test case if each player substracts 1 in his/her turn each time...the answer will be second..?

Utkarsh Saxena: 2014-12-30 12:10:33

uff!!.. my first game theory question.. nice :D

Deepak gupta: 2014-04-17 02:08:58

great problem :)

Shwetank sharad: 2013-07-13 19:01:16

someone please post some more test cases

Varun Jalan: 2010-02-07 07:24:35

just that number..not the whole row

Core2Duo: 2010-02-06 14:52:36

Yes. Is the number removed from that number only or from the whole row?

Ehor Nechiporenko: 2010-02-03 16:36:33

The player subtracts any number between 1 and K inclusive from it.
From what? From number?

Last edit: 2010-02-03 16:39:58

Added by:Varun Jalan
Time limit:0.343s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Resource:own problem used for Codechef Snackdown