Gerrymander

All submissions for this problem are available.
The country of BitLand is divided into N districts, and these districts are arranged in a circle: 1, 2, 3, ..., N, where i and i+1 are adjacent for all 1 ≤ i ≤ N1, and also 1 and N are adjacent. It is given that N = o_{1} * o_{2}, where o_{1} and o_{2} are odd integers.
There are only 2 political parties in BitLand: the Zeros and the Ones. There was an election, in which each district chose it's representative who is either a Zero or a One. We know this data. i.e. for each of the N districts, we know whether their representative is a Zero or a One.
The N districts should be partitioned into o_{1} states, where each state consists of o_{2} consecutive districts.
For example, if o_{1} = 5 and o_{2}=3, then N=15, and {1,2,3} would be a valid state. {2,3,4}, {13,14,15}, {14,15,1}, {15,1,2} are other examples of valid states. But {3,5,6} is not a valid state, because the districts are not consecutive.
A state gets a One Governor if, among all the o_{2} district representatives belonging to it, there are more One district representatives than Zero representatives. And it gets a Governor who is from the Zero party, if the majority of its district representatives are from the Zero party. And because o_{2} is odd, there will be no ties.
The President of BitLand will be a One if the majority of the o_{1} state Governors are Ones. Otherwise, the President will be from the Zero party.
But the state boundaries have not been fixed yet. Given just the districtwise data (i.e. whether each district's representative is a Zero or a One), you need to find if there is a way to partition them into states such that the President is a One.
Input
 The first line contains one integer, T, which is the number of testcases.
 The first line of each testcase contains two space separated integers, o_{1} and o_{2}, which are the number of states, and number of districts in each state, respectively.
 The next line of each testcase contains N = o_{1} * o_{2} space separated integers: d_{1}, d_{2}, .., d_{N}. If d_{i} is 1, then it signifies that District i has chosen a One representative. If d_{i} is 0, then they have a Zero representative.
Output
 Each testcase should be in a new line, and should contain 1, if the President can be a One, and 0 otherwise.
Constraints
For all subtasks you may assume that:
 1 ≤ T ≤ 100
 o_{1},o_{2} will be odd positive integers.
 1 ≤ Summation of o_{1}*o_{2} over all testcases ≤ 10^{6}
 0 ≤ d_{i} ≤ 1
Subtask 1: For 10% of the score,
 1 ≤ Summation of o_{1}*o_{2} over all testcases ≤ 10^{4}
Subtask 2: For further 20% of the score,
 1 ≤ o_{1} ≤ 10^{4}
 1 ≤ o_{2} ≤ 10^{2}
Subtask 3: For further 70% of the score,
 No further constraints.
Example
Input: 4 5 1 1 0 0 1 1 3 3 0 0 1 1 0 1 1 0 0 3 3 1 1 1 0 1 0 0 1 0 3 3 1 0 0 1 1 0 1 0 0 Output: 1 1 1 0
Explanation
In the first testcase, each state should have only 1 district, and hence, there is no actual choice in constructing the states. There will be three One Governors, and two Zero Governors, and hence the President will be a One.
In the second testcase, each of the three states should should have 3 districts each. Consider the following partitioning of the districts into states: {2,3,4}, {5,6,7} and {8,9,1}. So, the first state consists of the districts {2,3,4}, and the representatives of these correspond to {0,1,1}. The majority is One, and hence the first state will have a One Governor. The representatives corresponding to the second state are {0,1,1}, and so again, this will have a One Governor. The third state has representatives {0,0,0}, and hence will have a Zero Governor. On the whole, there are two One Governors, and one Zero Governor, and hence the President will be a One. And since there is a way to partition the districts into states, in which the President is a One, the answer is 1.
In the third testcase, each of the three states should should have 3 districts each. Consider the following partitioning of the districts into states: {3,4,5}, {6,7,8} and {9,1,2}. So, the first state consists of the districts {3,4,5}, and the representatives of these correspond to {1,0,1}. The majority is One, and hence the first state will have a One Governor. The representatives corresponding to the second state are {0,0,1}, and since the majority is Zero, this will have a Zero Governor. The third state has representatives {0,1,1}, and as Ones are in majority, this will have a One Governor. On the whole, there are two One Governors, and one Zero Governor, and hence the President will be a One. And since there is a way to partition the districts into states, in which the President is a One, the answer is 1.
In the fourth testcase, you can check that no matter how you construct the states, the President cannot be a One. Hence, the answer is 0.
Author:  admin2 
Tags  admin2 
Date Added:  9022017 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.5, PYPY, 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, SCM chicken, CLOJ, FS 
Comments
 Please login at the top to post a comment.
SUCCESSFUL SUBMISSIONS
Fetching successful submissions
HELP
If you are still having problems, see a sample solution here. 