This documentation is automatically generated by online-judge-tools/verification-helper
// verification-helper: PROBLEM https://judge.yosupo.jp/problem/bitwise_xor_convolution
#include <bits/stdc++.h>
using namespace std;
#define call_from_test
#include "../../mod/mint.cpp"
#include "../../convolution/bitwise/fwht.cpp"
#include "../../convolution/bitwise/xor.cpp"
#undef call_from_test
signed main(){
cin.tie(0);
ios::sync_with_stdio(0);
int n;
cin>>n;
using M = Mint<int, 998244353>;
int sz=1<<n;
vector<M> as(sz),bs(sz);
for(int i=0;i<sz;i++) cin>>as[i].v;
for(int i=0;i<sz;i++) cin>>bs[i].v;
fwht(as,bitwise_xor::zeta);
fwht(bs,bitwise_xor::zeta);
for(int i=0;i<sz;i++) as[i]*=bs[i];
fwht(as,bitwise_xor::zeta);
M inv=M(sz).inv();
for(int i=0;i<sz;i++) as[i]*=inv;
for(int i=0;i<sz;i++){
if(i) cout<<' ';
cout<<as[i];
}
cout<<endl;
return 0;
}
#line 1 "test/yosupo/bitwise_xor_convolution.test.cpp"
// verification-helper: PROBLEM https://judge.yosupo.jp/problem/bitwise_xor_convolution
#include <bits/stdc++.h>
using namespace std;
#define call_from_test
#line 1 "mod/mint.cpp"
#line 3 "mod/mint.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
template<typename T, T MOD = 1000000007>
struct Mint{
inline static constexpr T mod = MOD;
T v;
Mint():v(0){}
Mint(signed v):v(v){}
Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}
Mint pow(long long k){
Mint res(1),tmp(v);
while(k){
if(k&1) res*=tmp;
tmp*=tmp;
k>>=1;
}
return res;
}
static Mint add_identity(){return Mint(0);}
static Mint mul_identity(){return Mint(1);}
Mint inv(){return pow(MOD-2);}
Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}
Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}
Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}
Mint& operator/=(Mint a){return (*this)*=a.inv();}
Mint operator+(Mint a) const{return Mint(v)+=a;}
Mint operator-(Mint a) const{return Mint(v)-=a;}
Mint operator*(Mint a) const{return Mint(v)*=a;}
Mint operator/(Mint a) const{return Mint(v)/=a;}
Mint operator+() const{return *this;}
Mint operator-() const{return v?Mint(MOD-v):Mint(v);}
bool operator==(const Mint a)const{return v==a.v;}
bool operator!=(const Mint a)const{return v!=a.v;}
static Mint comb(long long n,int k){
Mint num(1),dom(1);
for(int i=0;i<k;i++){
num*=Mint(n-i);
dom*=Mint(i+1);
}
return num/dom;
}
};
template<typename T, T MOD>
ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;}
//END CUT HERE
#ifndef call_from_test
signed main(){
return 0;
}
#endif
#line 1 "convolution/bitwise/fwht.cpp"
#line 3 "convolution/bitwise/fwht.cpp"
using namespace std;
#endif
// https://kazuma8128.hatenablog.com/entry/2018/05/31/144519
//BEGIN CUT HERE
// O(n \log n)
template<typename T, typename F>
void fwht(vector<T> &as,F f){
int n=as.size();
for(int d=1;d<n;d<<=1)
for(int m=d<<1,i=0;i<n;i+=m)
for(int j=0;j<d;j++)
f(as[i+j],as[i+j+d]);
}
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
signed main(){
return 0;
}
#endif
#line 1 "convolution/bitwise/xor.cpp"
#line 3 "convolution/bitwise/xor.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
namespace bitwise_xor{
auto zeta=[](auto& lo,auto& hi){
auto x=lo+hi,y=lo-hi;
lo=x;
hi=y;
};
auto moebius=[](auto& lo,auto& hi){
auto x=lo+hi,y=lo-hi;
lo=x/decltype(x)(2);
hi=y/decltype(y)(2);
};
}
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
signed main(){
return 0;
}
#endif
#line 10 "test/yosupo/bitwise_xor_convolution.test.cpp"
#undef call_from_test
signed main(){
cin.tie(0);
ios::sync_with_stdio(0);
int n;
cin>>n;
using M = Mint<int, 998244353>;
int sz=1<<n;
vector<M> as(sz),bs(sz);
for(int i=0;i<sz;i++) cin>>as[i].v;
for(int i=0;i<sz;i++) cin>>bs[i].v;
fwht(as,bitwise_xor::zeta);
fwht(bs,bitwise_xor::zeta);
for(int i=0;i<sz;i++) as[i]*=bs[i];
fwht(as,bitwise_xor::zeta);
M inv=M(sz).inv();
for(int i=0;i<sz;i++) as[i]*=inv;
for(int i=0;i<sz;i++){
if(i) cout<<' ';
cout<<as[i];
}
cout<<endl;
return 0;
}