#define _USE_MATH_DEFINES #include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr ll LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 1000000007; // constexpr int MOD = 998244353; constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1}; constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios_base::sync_with_stdio(false); cout << fixed << setprecision(20); } } iosetup; struct SqrtDecomposition { int b, b_n; std::vector left, right; std::vector need_to_be_eval; SqrtDecomposition(int n) : b(std::sqrt(n)) { b_n = (n + b - 1) / b; left.resize(b_n); right.resize(b_n); need_to_be_eval.assign(b_n, false); for (int i = 0; i < b_n; ++i) { left[i] = b * i; right[i] = i + 1 == b_n ? n : b * (i + 1); } } template void partial_update(int idx, T val); template void total_update(int idx, T val); template void update(int l, int r, T val) { if (r <= l) return; int l_b = l / b, r_b = (r - 1) / b; if (l_b == r_b) { for (int i = l; i < r; ++i) partial_update(i, val); } else { for (int i = l; i < right[l_b]; ++i) partial_update(i, val); for (int i = l_b + 1; i < r_b; ++i) total_update(i, val); for (int i = left[r_b]; i < r; ++i) partial_update(i, val); } } void partial_query(int idx, pair &val); void total_query(int idx, pair &val); pair query(int l, int r, pair UNITY) { int l_b = l / b, r_b = (r - 1) / b; pair res = UNITY; if (l_b == r_b) { for (int i = l; i < r; ++i) partial_query(i, res); } else if (l < r) { for (int i = l; i < right[l_b]; ++i) partial_query(i, res); for (int i = l_b + 1; i < r_b; ++i) total_query(i, res); for (int i = left[r_b]; i < r; ++i) partial_query(i, res); } return res; } }; vector len, deg; vector sum_x, sum_y; vector lazy; vector> theta; template void SqrtDecomposition::partial_update(int idx, T val) { int tmp = idx / b; if (need_to_be_eval[tmp]) { if (lazy[tmp] > 0) { FOR(i, left[tmp], right[tmp]) { theta[tmp][deg[i]] -= len[i]; (deg[i] += lazy[tmp]) %= 360; theta[tmp][deg[i]] += len[i]; } lazy[tmp] = 0; } need_to_be_eval[idx] = false; } sum_x[tmp] -= len[idx] * cos(deg[idx] * M_PI / 180); sum_y[tmp] -= len[idx] * sin(deg[idx] * M_PI / 180); theta[tmp][deg[idx]] -= len[idx]; (deg[idx] += val) %= 360; sum_x[tmp] += len[idx] * cos(deg[idx] * M_PI / 180); sum_y[tmp] += len[idx] * sin(deg[idx] * M_PI / 180); theta[tmp][deg[idx]] += len[idx]; } template void SqrtDecomposition::total_update(int idx, T val) { array nx{}; REP(i, 360) { if (theta[idx][i] > 0) { sum_x[idx] -= theta[idx][i] * cos(i * M_PI / 180); sum_y[idx] -= theta[idx][i] * sin(i * M_PI / 180); nx[(i + val) % 360] += theta[idx][i]; } } theta[idx].swap(nx); REP(i, 360) { if (theta[idx][i] > 0) { sum_x[idx] += theta[idx][i] * cos(i * M_PI / 180); sum_y[idx] += theta[idx][i] * sin(i * M_PI / 180); } } (lazy[idx] += val) %= 360; need_to_be_eval[idx] = true; } void SqrtDecomposition::partial_query(int idx, pair &val) { int tmp = idx / b; if (need_to_be_eval[tmp]) { if (lazy[tmp] > 0) { FOR(i, left[tmp], right[tmp]) { theta[tmp][deg[i]] -= len[i]; (deg[i] += lazy[tmp]) %= 360; theta[tmp][deg[i]] += len[i]; } lazy[tmp] = 0; } need_to_be_eval[idx] = false; } val.first += len[idx] * cos(deg[idx] * M_PI / 180); val.second += len[idx] * sin(deg[idx] * M_PI / 180); } void SqrtDecomposition::total_query(int idx, pair &val) { val.first += sum_x[idx]; val.second += sum_y[idx]; } int main() { int n, q; cin >> n >> q; SqrtDecomposition sd(n); len.assign(n, 1); deg.assign(n, 0); sum_x.resize(sd.b_n); sum_y.assign(sd.b_n, 0); lazy.assign(sd.b_n, 0); theta.resize(sd.b_n); REP(i, sd.b_n) { sum_x[i] = sd.right[i] - sd.left[i]; theta[i][0] = sd.right[i] - sd.left[i]; } while (q--) { int query; cin >> query; if (query == 0) { int i, x; cin >> i >> x; --i; sd.update(i, n, (x - deg[i] + 360) % 360); } else if (query == 1) { int i, x; cin >> i >> x; --i; int tmp = i / sd.b; sd.partial_update(i, 0); sum_x[tmp] -= len[i] * cos(deg[i] * M_PI / 180); sum_y[tmp] -= len[i] * sin(deg[i] * M_PI / 180); theta[tmp][deg[i]] -= len[i]; len[i] = x; sum_x[tmp] += len[i] * cos(deg[i] * M_PI / 180); sum_y[tmp] += len[i] * sin(deg[i] * M_PI / 180); theta[tmp][deg[i]] += len[i]; } else if (query == 2) { int i; cin >> i; --i; auto [ans_x, ans_y] = sd.query(0, i + 1, {0, 0}); cout << ans_x << ' ' << ans_y << '\n'; } // REP(i, sd.b_n) cout << '(' << sum_x[i] << ',' << sum_y[i] << ')' << " \n"[i + 1 == sd.b_n]; } return 0; }