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#include <bits/stdc++.h> | |
#define all(x) (x).begin(), (x).end() | |
using namespace std; | |
using ll = long long; | |
constexpr ll mod = 1e9+9; | |
template<class T, class U> T fpow(T _base, U _pow, T _mod){_base %= _mod; T _x = 1; for(; _pow > 0; _pow >>= 1){ if(_pow&1) _x = _x*_base%_mod; _base = _base*_base%_mod;} return _x;} | |
template<class T> T divmod(T _a, T _b, T _mod){return _a*fpow(_b, _mod-2, _mod)%_mod;} | |
template<class T> struct M2{ | |
T w, x, y, z, det; | |
M2(T a, T b, T c, T d){ | |
w = a, x = b, y = c, z = d; | |
det = divmod(1LL, w*z-x*y, mod); | |
} | |
}; | |
const M2<ll> M[] = {{1, 1, 1, 0}, {0, 1, 1, 1}, {1, 1, 1, -1}}; | |
// OR AND XOR | |
template<class T> void go(vector<T> &v, bool inv, int k){ | |
int n = (int)size(v); | |
for(int len = 1, bit = 0; len < n; len *= 2, bit = (bit+1)%k){ | |
for(int pos = 0; pos < n; pos += len*2){ | |
for(int i = 0; i < len; i++){ | |
T &a = v[pos+i]; | |
T &b = v[pos+i+len]; | |
if(!inv) | |
tie(a, b) = make_pair((M[bit].w*a+M[bit].x*b)%mod, (M[bit].y*a+M[bit].z*b)%mod); | |
else | |
tie(a, b) = make_pair((M[bit].z*a-M[bit].y*b)%mod * M[bit].det % mod, (M[bit].w*b-M[bit].x*a)%mod * M[bit].det % mod); | |
} | |
} | |
} | |
} | |
template<class T> void mul(vector<T> &va, vector<T> &vb, int k){ | |
int n = (int)size(va); | |
n = 2<<__lg(n-1); | |
if(__builtin_ctz(n)&1) | |
n <<= 1; | |
va.resize(n), vb.resize(n); | |
go(va, 0, k); go(vb, 0, k); | |
for(int i = 0; i < n; i++){ | |
va[i] *= vb[i]; | |
va[i] %= mod; | |
} | |
go(va, 1, k); | |
} | |
int main(){ | |
ios_base::sync_with_stdio(0); | |
cin.tie(0); | |
int n; cin>>n; | |
vector<ll> a(n), b(n); | |
for(int i = 0; i < n; i++) | |
cin>>a[i]; | |
for(int i = 0; i < n; i++) | |
cin>>b[i]; | |
mul(a, b, 3); | |
int m = (int)size(a); | |
while(m and !a[m-1]) | |
m--; | |
for(int i = 0; i < m; i++){ | |
if(a[i] < 0) a[i] += mod; | |
cout<<a[i]<<' '; | |
} | |
} |
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