#include"game.h"
#include<string.h>
#include<vector>
using namespace std;
typedef vector<int> vi;
int n;
string t;
int sum;
int get(vi v){int siz;t=string(n,'1');siz=0;for(int x:v){if(x>n)break;t[x-1]='0';siz++;}return(siz-guess(t)+sum)/2;
}
vi al(int n){vi v;for(int i=1;i<=n;i++)v.push_back(i);return v;
}
vi sh(vi a,int b){for(int&x:a)x+=b;return a;
}
bool us[6010];
vi inv(vi a,int n){vi c;memset(us,0,n+1);for(int x:a)us[x]=1;for(int i=1;i<=n;i++){if(!us[i])c.push_back(i);}return c;
}
vi operator+(vi a,vi b){a.insert(a.end(),b.begin(),b.end());return a;
}
struct sol{int n;vector<vi>a;void add(vi v){a.push_back(v);}
}w[20];
void pre(){int n,k,i,j;vi t;w[1]={2,{{1},{1,2}}};for(i=2;i<=10;i++){k=w[i-1].a.size();n=w[i-1].n;w[i].n=n*2+k-1;for(j=0;j<k-1;j++){vi&u=w[i-1].a[j];w[i].add(u+sh(u,n));t=inv(u,n)+sh(u,n);t.push_back(n*2+j+1);w[i].add(t);}w[i].add(al(n));w[i].add(al(w[i].n));}
}
int res[6010];
void solve(int sh,int id,vi r){if(id==1){res[sh+1]=r[0];res[sh+2]=r[1]-r[0];return;}int n,k,i,c,t,al;vi ra,rb;n=w[id-1].n;k=w[id-1].a.size();c=r[k*2-2];al=r[k*2-1]-c;for(i=0;i<k-1;i++){t=res[sh+n*2+i+1]=((r[i*2]+r[i*2+1])^c)&1;al-=t;rb.push_back(t=(r[i*2]+r[i*2+1]-t-c)/2);ra.push_back(r[i*2]-t);}ra.push_back(c);rb.push_back(al);solve(sh,id-1,ra);solve(sh+n,id-1,rb);
}
const int mx=10;
string game(int _n,int k){n=_n;vi r;string s(n,'1');pre();sum=guess(s);for(vi v:w[mx].a)r.push_back(get(v));solve(0,mx,r);for(int i=0;i<n;i++)s[i]=res[i+1]+'0';return s;
}