#pragma region satashun // #pragma GCC optimize("Ofast") // #pragma GCC optimize("unroll-loops") #include using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; using pii = pair; template using V = vector; template using VV = V>; template V make_vec(size_t a) { return V(a); } template auto make_vec(size_t a, Ts... ts) { return V(ts...))>(a, make_vec(ts...)); } template void fill_vec(T& v, const V& val) { v = val; } template void fill_vec(vector& vec, const V& val) { for (auto& v : vec) fill_vec(v, val); } #define pb push_back #define eb emplace_back #define mp make_pair #define fi first #define se second #define rep(i, n) rep2(i, 0, n) #define rep2(i, m, n) for (int i = m; i < (n); i++) #define per(i, b) per2(i, 0, b) #define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--) #define ALL(c) (c).begin(), (c).end() #define SZ(x) ((int)(x).size()) constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); } template void chmin(T& t, const U& u) { if (t > u) t = u; } template void chmax(T& t, const U& u) { if (t < u) t = u; } template int arglb(const V& v, const T& x) { return distance(v.begin(), lower_bound(ALL(v), x)); } template int argub(const V& v, const T& x) { return distance(v.begin(), upper_bound(ALL(v), x)); } template void mkuni(vector& v) { sort(ALL(v)); v.erase(unique(ALL(v)), end(v)); } template vector sort_by(const vector& v, bool increasing = true) { vector res(v.size()); iota(res.begin(), res.end(), 0); if (increasing) { stable_sort(res.begin(), res.end(), [&](int i, int j) { return v[i] < v[j]; }); } else { stable_sort(res.begin(), res.end(), [&](int i, int j) { return v[i] > v[j]; }); } return res; } // prototype template ostream& operator<<(ostream& os, const pair& p); template ostream& operator<<(ostream& os, const vector& v); template istream& operator>>(istream& is, vector& v); template ostream& operator<<(ostream& os, const array& arr); template ostream& operator<<(ostream& os, const set& ST); template ostream& operator<<(ostream& os, const multiset& ST); template ostream& operator<<(ostream& os, const map& MP); ostream& operator<<(ostream& o, __int128_t x); // io functions template istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template ostream& operator<<(ostream& os, const pair& p) { os << "(" << p.first << "," << p.second << ")"; return os; } template istream& operator>>(istream& is, vector& v) { for (auto& x : v) { is >> x; } return is; } template ostream& operator<<(ostream& os, const vector& v) { os << "{"; rep(i, v.size()) { if (i) os << ","; os << v[i]; } os << "}"; return os; } template ostream& operator<<(ostream& os, const array& arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template ostream& operator<<(ostream& os, const set& ST) { os << "{"; for (auto it = ST.begin(); it != ST.end(); ++it) { if (it != ST.begin()) os << ","; os << *it; } os << "}"; return os; } template ostream& operator<<(ostream& os, const multiset& ST) { os << "{"; for (auto it = ST.begin(); it != ST.end(); ++it) { if (it != ST.begin()) os << ","; os << *it; } os << "}"; return os; } template ostream& operator<<(ostream& os, const map& MP) { for (auto it = MP.begin(); it != MP.end(); ++it) { os << "(" << it->first << ": " << it->second << ")"; } return os; } string to_string(__int128_t x) { if (x == 0) return "0"; string result; if (x < 0) { result += "-"; x *= -1; } string t; while (x) { t.push_back('0' + x % 10); x /= 10; } reverse(t.begin(), t.end()); return result + t; } ostream& operator<<(ostream& o, __int128_t x) { return o << to_string(x); } #ifdef LOCAL void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << " " << H; debug_out(T...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif template V& operator+=(V& vec, const T& v) { for (auto& x : vec) x += v; return vec; } template V& operator-=(V& vec, const T& v) { for (auto& x : vec) x -= v; return vec; } // suc : 1 = newline, 2 = space template void print(T x, int suc = 1) { cout << x; if (suc == 1) cout << "\n"; else if (suc == 2) cout << " "; } template void print(const vector& v, int suc = 1) { for (int i = 0; i < v.size(); ++i) print(v[i], i == int(v.size()) - 1 ? suc : 2); } template void show(T x) { print(x, 1); } template void show(Head H, Tail... T) { print(H, 2); show(T...); } int topbit(int t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int botbit(int a) { return a == 0 ? 32 : __builtin_ctz(a); } int botbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); } int popcount(int t) { return __builtin_popcount(t); } int popcount(ll t) { return __builtin_popcountll(t); } int bit_parity(int t) { return __builtin_parity(t); } int bit_parity(ll t) { return __builtin_parityll(t); } struct prepare_io { prepare_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); } } prep_io; #pragma endregion satashun template struct ModInt { using uint = unsigned int; using ull = unsigned long long; using M = ModInt; uint v; ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); } M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD) v = (_v < MOD) ? _v : _v - MOD; return *this; } explicit operator bool() const { return v != 0; } explicit operator int() const { return v; } M operator+(const M& a) const { return M().set_norm(v + a.v); } M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); } M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); } M operator/(const M& a) const { return *this * a.inv(); } M& operator+=(const M& a) { return *this = *this + a; } M& operator-=(const M& a) { return *this = *this - a; } M& operator*=(const M& a) { return *this = *this * a; } M& operator/=(const M& a) { return *this = *this / a; } M operator-() const { return M() - *this; } M& operator++(int) { return *this = *this + 1; } M& operator--(int) { return *this = *this - 1; } M pow(ll n) const { if (n < 0) return inv().pow(-n); M x = *this, res = 1; while (n) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } M inv() const { ll a = v, b = MOD, p = 1, q = 0, t; while (b != 0) { t = a / b; swap(a -= t * b, b); swap(p -= t * q, q); } return M(p); } friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; } friend istream& operator>>(istream& in, M& x) { ll v_; in >> v_; x = M(v_); return in; } bool operator<(const M& r) const { return v < r.v; } bool operator>(const M& r) const { return v < *this; } bool operator<=(const M& r) const { return !(r < *this); } bool operator>=(const M& r) const { return !(*this < r); } bool operator==(const M& a) const { return v == a.v; } bool operator!=(const M& a) const { return v != a.v; } static uint get_mod() { return MOD; } }; // using Mint = ModInt<1000000007>; using Mint = ModInt<998244353>; template bool is_zero(T x) { return x == 0; } template bool is_one(T x) { return x == 1; } template struct Matrix { int H, W; VV a; Matrix() : H(0), W(0) {} Matrix(int H, int W) : H(H), W(W), a(VV(H, V(W))) {} Matrix(const VV& v) : H(v.size()), W(v[0].size()), a(v) {} static Matrix E(int n) { Matrix a(n, n); rep(i, n) a.set(i, i, 1); return a; } T at(int i, int j) const { return a[i][j]; } void set(int i, int j, T v) { a[i][j] = v; } Matrix operator+(const Matrix& r) const { assert(H == r.H && W == r.W); VV v(H, V(W)); rep(i, H) rep(j, W) v[i][j] = a[i][j] + r.a[i][j]; return Matrix(v); } Matrix operator-(const Matrix& r) const { assert(H == r.H && W == r.W); VV v(H, V(W)); rep(i, H) rep(j, W) v[i][j] = a[i][j] - r.a[i][j]; return Matrix(v); } Matrix operator*(const Matrix& r) const { assert(W == r.H); VV v(H, V(r.W)); rep(i, H) rep(k, W) rep(j, r.W) v[i][j] += a[i][k] * r.a[k][j]; return Matrix(v); } Matrix& operator+=(const Matrix& r) { return (*this) = (*this) + r; } Matrix& operator-=(const Matrix& r) { return (*this) = (*this) - r; } Matrix& operator*=(const Matrix& r) { return (*this) = (*this) * r; } /* 副作⽤がある, 基本的に⾃分でこれを呼ぶことはない 掃き出し法をする 左からvar列が掃き出す対象で、それより右は同時に値を変更するだけ(e.g. 逆⾏列 は右に単位⾏列おいてから掃き出す) ⾏swap, 列swap は⾏わない rank を返す */ int sweep(int var) { int rank = 0; vector used(H); rep(j, var) { int i = 0; while (i < H && (used[i] || is_zero(a[i][j]))) i++; if (i == H) continue; used[i] = true; rank++; T t = a[i][j]; rep(k, W) a[i][k] = a[i][k] / t; rep(k, H) if (k != i) { T t = a[k][j]; rep(l, W) a[k][l] = a[k][l] - a[i][l] * t; } } return rank; } Matrix pow(ll n) const { assert(H == W); int h = H; Matrix x = *this, res(h, h); res = E(h); while (n > 0) { if (n & 1) res *= x; x *= x; n >>= 1; } return res; } friend ostream& operator<<(ostream& o, const Matrix& A) { rep(i, A.H) { rep(j, A.W) o << A.a[i][j] << " "; o << endl; } return o; } }; void slv() { // input int N, X, Y; cin >> N >> X >> Y; V A(X), B(Y); cin >> A >> B; V ca(2), cb(2); for (int x : A) { ca[x % 2]++; } for (int x : B) { cb[x % 2]++; } // solve Mint ans; rep(i, 18) { Matrix a(2, 2); V ca(2), cb(2); for (int x : A) { ca[x >> i & 1]++; } for (int x : B) { cb[x >> i & 1]++; } rep(f, 2) { rep(p, 2) { rep(q, 2) { a.a[f][(f | p) & q] += ca[p] * cb[q]; } } } a = a.pow(N); ans += a.a[0][1] * Mint(2).pow(i); } show(ans); } int main() { int cases = 1; // cin >> cases; rep(i, cases) slv(); return 0; }