codechef 2011 aug infinite grid game

#include <algorithm>
#include <iostream>
#include <sstream>
#include <string>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cctype>
#include <cmath>
using namespace std;
typedef long long LL;
#define FOR(k,a,b) for(int k(a); k < (b); ++k)
#define REP(k,a) for(int k=0; k < (a); ++k)

int main()
{
    int T,m,n,p,q;
    vector<vector<int> > state(1001,vector<int> (1001));
    //0-1 m direction can win, 2-0 n direction, 4-0 diagonal
    //state[0][0] loose
    REP(i,1001)
    REP(j,1001)
    {
        if(i && ((state[i-1][j]&1) || !state[i-1][j]))
            state[i][j]|=1;
        if(j && ((state[i][j-1]&2)|| !state[i][j-1]))
            state[i][j]|=2;
        if(i && j && ((state[i-1][j-1]&4)|| !state[i-1][j-1]))
            state[i][j]|=4;
    }
    cin >> T;
    REP(testcase,T)
    {
        cin >> m >> n >> p >> q;
        m-=p;n-=q;
        if(state[m][n])
            cout << "Alice" << endl;
        else
            cout << "Bob" << endl;
    }
    return 0;
}