#include "datalab.h"

#include<bits/stdc++.h>
#define Gc() getchar()
#define Me(x,y) memset(x,y,sizeof(x))
#define Mc(x,y) memcpy(x,y,sizeof(x))
#define d(x,y) ((m)*(x-1)+(y))
#define R(n) (rnd()%(n)+1)
#define Pc(x) putchar(x)
#define LB lower_bound
#define UB upper_bound
#define fi first
#define se second
#define eb emplace_back
#define all(x) x.begin(),x.end()
using namespace std;using ll=long long;using db=double;using lb=long db;using ui=unsigned;using ull=unsigned long long;using pii=pair<int,int>;
const int N=2e6+5,M=3e5+5,K=1000+5,mod=998244353,Mod=mod-1;const db eps=1e-9;const int INF=1e9+7;mt19937 rnd(28382);
#define Tp template<typename T>
#define Ts template<typename T,typename... Ar>
namespace Debug{
	Tp void _debug(char* f,T t){cerr<<f<<'='<<t<<endl;}
	Ts void _debug(char* f,T x,Ar... y){while(*f!=',') cerr<<*f++;cerr<<'='<<x<<",";_debug(f+1,y...);}
	#ifdef LOCAL
	#define gdb(...) _debug((char*)#__VA_ARGS__,__VA_ARGS__)
	#else 
	#define gdb(...) void()
	#endif
}using namespace Debug;
int sgn[N];
using vec=bitset<8192>;
vector<int> solve(int k,int LIMIT){
	vector<int> sgn(k),op(k);
	sgn[k-1]=1;sgn[k-2]=-1;
	for(int t=1;t<=100;t++){
		vec x,y;
		for(int j=0;j<k;j++) x[j]=R(2)-1,y[j]=R(2)-1;
		vec z=Add(x,y);
		// gdb(x[0],x[1],x[2],x[3],y[0],y[1],y[2],y[3],z[0],z[1],z[2],z[3]);
		int R=0,L=0;
		while(R<k-2){
			int w=x[R]+y[R]+L;
			L=0;
			if(0<=w&&w<2){R++;continue;}
			// gdb(x[R],y[R],z[R],w,L);
			L=(w<0?-1:1);
			int p=x[R+1]+y[R+1];
			// if(!~R) gdb(R);
			if(p==0){
				if((x[R+2]+y[R+2])%2!=z[R+2]) op[R]=-L,L=-1;
				else op[R]=L,L=1;
			}else{
				if((x[R+2]+y[R+2])%2!=z[R+2]) op[R]=L,L=1;
				else op[R]=-L,L=-1;
			}
			R++;
		}
	}
	for(int i=k-3;~i;i--){
		if(op[i]){
			// gdb(i);
			sgn[i]=sgn[i+1]*op[i];
			continue;
		}
		vec f;
		f.reset();
		f[i]=1;
		vec g=Add(f,f);
		int flag=0;
		for(int j=i+2;j<k;j++) flag|=g[j];
		if(!flag) sgn[i]=sgn[i+1];
		else sgn[i]=-sgn[i+1];
	}
	// gdb(sgn[0],sgn[1],sgn[2],sgn[3]);
	return sgn;
}