This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> pi;
typedef vector<int> vi;
typedef vector<pi> vpi;
#define pb emplace_back
#define mp make_pair
#define f first
#define s second
#define SZ(x) (int)x.size()
#define ALL(x) x.begin(),x.end()
#define lb lower_bound
const int MAXN=1001000;
const ll MOD=998244353;
int N,K,T;
string S;
void tobin(int y,int len){
string x;
while(y){
x+=('0' + y%2);
y/=2;
}
while(SZ(x) < len)x+='0';
reverse(ALL(x));
cout<<x;
}
vector<int> generate(int N,int K){
// cerr<<N<<' '<<K<<'\n';
int mod=(1<<(N-K+1));
vi A;
A.resize((1<<N),0);
ll alen=(K-1);
int ind=0;
int backf = min(K-1, N-K+1);
int frontf = K-backf;
if(frontf%2==0){
++frontf;
--backf;
}
// cerr<<backf<<' '<<frontf<<'\n';
vi B;
if(frontf > 1){
B = generate(K-1, frontf);
// for(auto i:B)cerr<<i<<' ';cerr<<'\n';
}
int ind2=0;
for(int i=1;i<=(1<<alen);++i){
for(int j=0;j<mod-1;++j){
A[ind] += ((1<<alen) - 1) * mod;
++ind;
// A.pb(A.back() ^ ((1<<alen)-1));
}
if(frontf == 1) A[ind] += (i&(-i))*mod;
else{
A[ind] += B[ind2]*mod;
++ind2;
}
++ind;
// flip A back
// if(SZ(A) < (1<<N))A.pb(A.back() ^ (i&(-i)));
}
// for(auto i:A)cerr<<i<<' ';cerr<<'\n';
ind=0;
for(int i=1;i<=(1<<alen);++i){
for(int j=1;j<mod;++j){
// B.pb(B.back() ^ (j&(-j)));
A[ind] += (j&(-j));
++ind;
}
A[ind] += (1<<backf)-1;
++ind;
// flip A back
// if(SZ(B) < (1<<N))B.pb(B.back() ^ ((1<<(K-1))-1));
}
// for(auto i:A)cerr<<i<<' ';cerr<<'\n';
return A;
}
int main(){
ios_base::sync_with_stdio(0);cin.tie(0);
cin>>N>>K>>T>>S;
if(K%2==0){
cout<<-1;
return 0;
}
ll v=0;ll k=1;
while(SZ(S)){
if(S.back() == '1')v+=k;
k*=2;
S.pop_back();
}
vi A = generate(N,K);
cout<<(1<<N)<<'\n';
tobin(v,N);cout<<'\n';
for(int i=0;i<((1<<N)-1);++i){
v ^= A[i];
tobin(v,N);cout<<'\n';
}
// for(int i=0;i<SZ(A);++i){
// // if(flip&&i%2){
// // A[i]=((1<<(K-1))-1)^A[i];
// // B[i]=((1<<(N-K+1))-1)^B[i];
// // }
// tobin(B[i],(N-K+1));
// tobin(A[i],K-1);
// cout<<'\n';
// }
}
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