#ifndef HIDDEN_IN_VS // 折りたたみ用 // 警告の抑制 #define _CRT_SECURE_NO_WARNINGS // ライブラリの読み込み #include using namespace std; // 型名の短縮 using ll = long long; // -2^63 ~ 2^63 = 9 * 10^18(int は -2^31 ~ 2^31 = 2 * 10^9) using pii = pair; using pll = pair; using pil = pair; using pli = pair; using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; using vb = vector; using vvb = vector; using vvvb = vector; using vc = vector; using vvc = vector; using vvvc = vector; using vd = vector; using vvd = vector; using vvvd = vector; template using priority_queue_rev = priority_queue, greater>; using Graph = vvi; // 定数の定義 const double PI = acos(-1); const vi DX = { 1, 0, -1, 0 }; // 4 近傍(下,右,上,左) const vi DY = { 0, 1, 0, -1 }; int INF = 1001001001; ll INFL = 4004004003104004004LL; // (int)INFL = 1010931620; double EPS = 1e-15; // 入出力高速化 struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp; // 汎用マクロの定義 #define all(a) (a).begin(), (a).end() #define sz(x) ((int)(x).size()) #define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x)) #define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x)) #define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");} #define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順 #define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順 #define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順 #define repe(v, a) for(const auto& v : (a)) // a の全要素(変更不可能) #define repea(v, a) for(auto& v : (a)) // a の全要素(変更可能) #define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d ビット全探索(昇順) #define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て(昇順) #define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod #define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去 #define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了 #define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定 // 汎用関数の定義 template inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; } template inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら true を返す) template inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら true を返す) template inline T get(T set, int i) { return (set >> i) & T(1); } // 演算子オーバーロード template inline istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template inline istream& operator>>(istream& is, vector& v) { repea(x, v) is >> x; return is; } template inline vector& operator--(vector& v) { repea(x, v) --x; return v; } template inline vector& operator++(vector& v) { repea(x, v) ++x; return v; } #endif // 折りたたみ用 #if __has_include() #include using namespace atcoder; #ifdef _MSC_VER #include "localACL.hpp" #endif //using mint = modint1000000007; using mint = modint998244353; //using mint = modint; // mint::set_mod(m); namespace atcoder { inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; } inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; } } using vm = vector; using vvm = vector; using vvvm = vector; using vvvvm = vector; #endif #ifdef _MSC_VER // 手元環境(Visual Studio) #include "local.hpp" #else // 提出用(gcc) inline int popcount(int n) { return __builtin_popcount(n); } inline int popcount(ll n) { return __builtin_popcountll(n); } inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; } inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; } inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; } inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; } #define gcd __gcd #define dump(...) #define dumpel(v) #define dump_list(v) #define dump_mat(v) #define input_from_file(f) #define output_to_file(f) #define Assert(b) { if (!(b)) while (1) cout << "OLE"; } #endif int naive(int h, int w, vl r, vl c, vvl a) { auto b(a); rep(i, h) repir(j, w - 1, 0) b[i][j] ^= b[i][0]; repir(i, h - 1, 0) rep(j, w) b[i][j] ^= b[0][j]; rep(i, h) rep(j, w) if (b[i][j]) return INF; int res = INF; ll a_max = 0; rep(i, h) rep(j, w) chmax(a_max, a[i][j]); rep(x0, (1LL << (msb(a_max) + 1))) { vl x(h), y(w); x[0] = x0; rep(j, w) y[j] = a[0][j] ^ x[0]; rep(i, h) x[i] = a[i][0] ^ y[0]; int c0 = 0, c1 = 0, c2 = 0, cINF = 0; rep(i, h) { if (x[i] == 0) c0++; else if (x[i] <= r[i]) c1++; else if (msb(x[i]) == msb(r[i])) c2++; else cINF++; } rep(j, w) { if (y[j] == 0) c0++; else if (y[j] <= c[j]) c1++; else if (msb(y[j]) == msb(c[j])) c2++; else cINF++; } dump(x0, ":", c0, c1, c2, cINF); if (cINF > 0) continue; chmin(res, c1 + 2 * c2); } return res; } int WA_TLE(int h, int w, vl r, vl c, vvl a) { auto b(a); rep(i, h) repir(j, w - 1, 0) b[i][j] ^= b[i][0]; repir(i, h - 1, 0) rep(j, w) b[i][j] ^= b[0][j]; rep(i, h) rep(j, w) if (b[i][j]) return INF; int res = INF; // x[i0] = 0 にする場合 rep(i0, h) { vl x(h), y(w); rep(j, w) y[j] = a[i0][j] ^ x[i0]; rep(i, h) x[i] = a[i][0] ^ y[0]; int c0 = 0, c1 = 0, c2 = 0, cINF = 0; rep(i, h) { if (x[i] == 0) c0++; else if (x[i] <= r[i]) c1++; else if (msb(x[i]) == msb(r[i])) c2++; else cINF++; } rep(j, w) { if (y[j] == 0) c0++; else if (y[j] <= c[j]) c1++; else if (msb(y[j]) == msb(c[j])) c2++; else cINF++; } if (cINF > 0) continue; chmin(res, c1 + 2 * c2); } // y[j0] = 0 にする場合 rep(j0, w) { vl x(h), y(w); rep(i, h) x[i] = a[i][j0] ^ y[j0]; rep(j, w) y[j] = a[0][j] ^ x[0]; int c0 = 0, c1 = 0, c2 = 0, cINF = 0; rep(i, h) { if (x[i] == 0) c0++; else if (x[i] <= r[i]) c1++; else if (msb(x[i]) == msb(r[i])) c2++; else cINF++; } rep(j, w) { if (y[j] == 0) c0++; else if (y[j] <= c[j]) c1++; else if (msb(y[j]) == msb(c[j])) c2++; else cINF++; } if (cINF > 0) continue; chmin(res, c1 + 2 * c2); } return res; } //【XOR 区間の分割】O(log max(r, c)) /* * 集合 {x∈[0..∞) | l ≦ x XOR c < r} を O(log max(r, c)) 個の半開区間に分割し,そのリストを返す. */ template vector> XOR_interval_division(T l, T r, T c) { chmax(l, T(0)); if (l >= r) return vector>(); int n = max(msb(r), msb(c)); vector> lrs; T val_l = 0, val_r = 0; bool eq = true; repir(i, n, 0) { T lb = get(l, i), rb = get(r, i), cb = get(c, i); if (eq) { if (lb != rb) eq = false; } else { if (!lb) { T val_l2 = val_l + ((1 ^ cb) << i); lrs.emplace_back(val_l2, val_l2 + (T(1) << i)); } if (rb) { T val_r2 = val_r + ((0 ^ cb) << i); lrs.emplace_back(val_r2, val_r2 + (T(1) << i)); } } val_l += (lb ^ cb) << i; val_r += (rb ^ cb) << i; } lrs.emplace_back(val_l, val_l + 1); return lrs; } int solve(int h, int w, vl r, vl c, vvl a) { auto b(a); rep(i, h) repir(j, w - 1, 0) b[i][j] ^= b[i][0]; repir(i, h - 1, 0) rep(j, w) b[i][j] ^= b[0][j]; rep(i, h) rep(j, w) if (b[i][j]) return INF; map ev; rep(j, w) { ev[0 ^ a[0][j]] += 0; ev[(0 ^ a[0][j]) + 1] -= 0; auto lrs = XOR_interval_division(1, c[j] + 1, a[0][j]); for (auto [l, r] : lrs) { dump(l, r, 1); ev[l] += 1; ev[r] -= 1; } lrs = XOR_interval_division(c[j] + 1, 1LL << (msb(c[j]) + 1), a[0][j]); for (auto [l, r] : lrs) { dump(l, r, 2); ev[l] += 2; ev[r] -= 2; } lrs = XOR_interval_division(1LL << (msb(c[j]) + 1), 1LL << 30, a[0][j]); for (auto [l, r] : lrs) { // dump(l, r, INF); ev[l] += INF; ev[r] -= INF; } } rep(i, h) { ev[0 ^ a[i][0] ^ a[0][0]] += 0; ev[(0 ^ a[i][0] ^ a[0][0]) + 1] -= 0; auto lrs = XOR_interval_division(1, r[i] + 1, a[i][0] ^ a[0][0]); for (auto [l, r] : lrs) { dump(l, r, 1); ev[l] += 1; ev[r] -= 1; } lrs = XOR_interval_division(r[i] + 1, 1LL << (msb(r[i]) + 1), a[i][0] ^ a[0][0]); for (auto [l, r] : lrs) { dump(l, r, 2); ev[l] += 2; ev[r] -= 2; } lrs = XOR_interval_division(1LL << (msb(r[i]) + 1), 1LL << 30, a[i][0] ^ a[0][0]); for (auto [l, r] : lrs) { // dump(l, r, INF); ev[l] += INF; ev[r] -= INF; } } dump(ev); ll res = INF; ll acc = 0; for (auto [val, cost] : ev) { if (val == (1LL << 30)) break; acc += cost; chmin(res, acc); dump(acc); } return (int)min(res, INF); } void bug_find() { #ifdef _MSC_VER // 合わない入力例を見つける. mt19937_64 mt; mt.seed((int)time(NULL)); uniform_int_distribution rnd(0LL, 1LL << 60); mute_dump = true; rep(hoge, 1000) { int M = 1 << 4; int h = rnd(mt) % 8 + 2; int w = rnd(mt) % 8 + 2; vl x(h), y(w); rep(i, h) x[i] = rnd(mt) % M; rep(j, w) y[j] = rnd(mt) % M; vvl a(h, vl(w)); rep(i, h) a[i][0] = rnd(mt) % (x[i] + 1); rep(j, w) a[0][j] = rnd(mt) % (y[j] + 1); repir(i, h - 1, 0) repir(j, w - 1, 1) a[i][j] = a[i][0] ^ a[0][j]; auto res_naive = naive(h, w, x, y, a); auto res_solve = solve(h, w, x, y, a); if (res_naive != res_solve) { cout << "----------error!----------" << endl; cout << "input:" << endl; cout << h << " " << w << endl; cout << x << endl; cout << y << endl; cout << a << endl; cout << "results:" << endl; cout << res_naive << endl; cout << res_solve << endl; cout << "--------------------------" << endl; } } mute_dump = false; exit(0); #endif } /* ----------error!---------- input: 4 4 3 26 26 10 13 23 4 20 4 5 5 21 17 16 16 0 15 14 14 30 9 8 8 24 results: 9 10 -------------------------- */ void Main() { int h, w; cin >> h >> w; vl x(h), y(w); cin >> x >> y; vvl a(h, vl(w)); cin >> a; dump(naive(h, w, x, y, a)); dump("---"); int res = solve(h, w, x, y, a); if (res == INF) res = -1; cout << res << endl; } int main() { input_from_file("input.txt"); // output_to_file("output.txt"); bug_find(); int t; cin >> t; // マルチテストケースの場合 // t = 1; // シングルテストケースの場合 while (t--) { dump("------------------------------"); Main(); } }