#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 998244353; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; typedef double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acos(-1.0); ll mod_pow(ll x, ll n, ll m=mod) { ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } ll gcd(ll a, ll b) { if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } ll mod_inverse(ll a) { return mod_pow(a, mod - 2,mod); } ll root[24], invroot[24]; void init() { rep(i, 24) { int n = (1 << i); root[i] = mod_pow(3, (mod - 1) / n,mod); invroot[i] = mod_inverse(root[i]); } } typedef vector poly; poly dft(poly f, bool inverse = false) { int n = f.size(); int i, j, k; //bit左右反転 for (i = 0, j = 1; j < n - 1; j++) { for (k = n >> 1; k > (i ^= k); k >>= 1); if (i > j)swap(f[i], f[j]); } for (int j = 1; (1 << j) <= n; j++) { int m = 1 << j; ll zeta = root[j]; if (inverse)zeta = invroot[j]; for (i = 0; i < n; i += m) { ll powzeta = 1; for (k = i; k < i + m / 2; k++) { ll t1 = f[k], t2 = powzeta * f[k + m / 2] % mod; f[k] = t1 + t2; while (f[k] >= mod)f[k] -= mod; f[k + m / 2] = t1 - t2 + mod; while (f[k + m / 2] >= mod)f[k + m / 2] -= mod; (powzeta *= zeta) %= mod; } } } if (inverse) { ll rv = mod_inverse(n); for (i = 0; i < n; i++) { (f[i] *= rv) %= mod; } } return f; } poly multiply(poly g, poly h) { int n = 1; int pi = 0, qi = 0; rep(i, g.size())if (g[i])pi = i; rep(i, h.size())if (h[i])qi = i; int sz = pi + qi + 2; while (n < sz)n *= 2; g.resize(n); h.resize(n); /*while (g.size() < n) { g.push_back(0); } while (h.size() < n) { h.push_back(0); }*/ poly gg = dft(g); poly hh = dft(h); poly ff; ff.resize(n); rep(i, n) { ff[i] = gg[i] * hh[i] % mod; } return dft(ff, true); } ll p; bool isr(int r) { int t = 1; vector cnt(p); rep(x, p - 1) { cnt[t]++; t = t * r % p; } rep1(i, p-1) { if (cnt[i] != 1)return false; } return true; } void solve() { init(); cin >> p; int r; rep1(i, p-1) { if (isr(i)) { r = i; break; } } vector trans(p); vector val(p); trans[1] = 0; int t = 1; val[0] = 1; rep1(i, p - 2) { t = t * r % p; trans[t] = i; val[i] = t; } poly a(p),b(p); rep1(i, p - 1)cin >> a[trans[i]]; rep1(i, p - 1)cin >> b[trans[i]]; vector ans(p); poly c = multiply(a, b); rep(i, c.size()) { ans[val[i%(p-1)]] += c[i]; } rep1(i, p - 1) { if (i > 1)cout << " "; cout << ans[i]; } cout << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(10); //init_f(); //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }