//@formatter:off #include #define rep(i,n) for (int i = 0; i < int(n); ++i) #define rrep(i,n) for (int i = int(n)-1; i >= 0; i--) #define rep2(i,s,n) for (int i = int(s); i < int(n); ++i) #define all(a) a.begin(),a.end() #define rall(a) a.rbegin(),a.rend() #define pb push_back #define eb emplace_back #define vi vector #define vvi vector> #define vl vector #define vvl vector> #define vd vector #define vvd vector> #define vs vector #define vc vector #define vvc vector> #define vb vector #define vvb vector> #define vp vector

#define vvp vector> using namespace std; using ll = long long; using P = pair; using LP = pair; template istream& operator>>(istream &is,pair &p) { return is >> p.first >> p.second; } template ostream& operator<<(ostream &os,const pair &p) { return os<<'{'< istream& operator>>(istream &is,vector &v) { for(T &t:v){is>>t;} return is; } template ostream& operator<<(ostream &os,const vector &v) { os<<'[';rep(i,v.size())os< bool chmin(T& a,T b) {if(a > b){a = b; return true;} return false;} template bool chmax(T& a,T b) {if(a < b){a = b; return true;} return false;} const int inf = 1001001001; const ll linf = 1001001001001001001; //@formatter:on template struct matrix { int h, w; vector> v; matrix(int h, int w, T t) : h(h), w(w), v(vector>(h, vector(w, t))) {} matrix(vector> v) : v(v), h(v.size()), w(v[0].size()) {} matrix &operator+=(const matrix &a) { rep(i, h) rep(j, w) v[i][j] += a.v[i][j]; return *this; } matrix &operator*=(const int &k) { rep(i, h) rep(j, w) v[i][j] *= k; return *this; } matrix &operator-=(const matrix &a) { *this += a * (-1); return *this; } matrix operator+(const matrix &a) const { auto res(*this); return res += a; } matrix operator*(const int &k) const { return res(*this) *= k; } matrix operator-(const matrix &a) const { return res(*this) -= a; } matrix operator*(const matrix &a) const { assert(w == a.h); matrix res(h, a.w, 0); rep(i, h) rep(j, a.h) rep(k, a.w) res.v[i][k] += v[i][j] * a.v[j][k]; return res; } matrix &operator*=(const matrix &a) { return *this = *this * a; } matrix pow(ll t) const { matrix res(h, w, 0), a(*this); rep(i, h) res.v[i][i] = 1; while (t > 0) { if (t & 1) res *= a; t >>= 1; a *= a; } return res; } }; template class lazy_segtree { using V = typename Node::value_structure; using VT = typename V::value_type; using O = typename Node::operate_structure; using OT = typename O::value_type; int n; vector tree; void propagate(int k, int l, int r) { // if (tree[k].op.value == O::identity) return; if (k < n) { tree[k * 2].op.value = O::operate(tree[k * 2].op.value, tree[k].op.value); tree[k * 2 + 1].op = O::operate(tree[k * 2 + 1].op.value, tree[k].op.value); } OT ot = O::duplicate(tree[k].op.value, r - l); tree[k].value.value = Node::operate(tree[k].value.value, ot); tree[k].op.value = O::identity; } public: VT get(int i) { return Node::operate(tree[i].value.value, tree[i].op.value); } lazy_segtree(int _n, vector init = vector()) { n = 1; while (n < _n) n *= 2; tree.assign(n * 2, Node{V::identity, O::identity}); if (init.size()) rep(i, _n) tree[i + n].value.value = init[i]; rrep(i, n) tree[i].value.value = V::operate(tree[i * 2].value.value, tree[i * 2 + 1].value.value); } void update(int a, int b, OT x, int k = 1, int l = 0, int r = -1) { if (r == -1) r = n; propagate(k, l, r); if (a <= l && r <= b) { tree[k].op.value = O::operate(tree[k].op.value, x); propagate(k, l, r); } else if (a < r && l < b) { update(a, b, x, k * 2, l, (l + r) / 2); update(a, b, x, k * 2 + 1, (l + r) / 2, r); tree[k].value.value = V::operate(tree[k * 2].value.value, tree[k * 2 + 1].value.value); } } // segment [a,b) VT fold(int a, int b, int k = 1, int l = 0, int r = -1) { if (r == -1) r = n; propagate(k, l, r); if (b <= l || r <= a) return V::identity; if (a <= l && r <= b) return tree[k].value.value; VT lt = fold(a, b, k * 2, l, (l + r) / 2); VT rt = fold(a, b, k * 2 + 1, (l + r) / 2, r); return V::operate(lt, rt); } }; using mat = matrix; const mat mat_id = matrix(vvd({{1, 0}, {0, 1}})); const mat vec_id = matrix(2, 1, 0); class Value_structure { public: using value_type = pair; value_type value; Value_structure(value_type value) : value(value) {} static const value_type identity; static const value_type operate(const value_type &l, const value_type &r) { return make_pair(r.first * l.first, r.first * l.second + r.second); } }; const pair Value_structure::identity = make_pair(mat_id, vec_id); class Operate_structure { public: using value_type = pair; value_type value; Operate_structure(value_type value) : value(value) {} static const value_type identity; static const value_type operate(const value_type &l, const value_type &r) { return make_pair(r.first * l.first, r.first * l.second + r.second); } static const value_type duplicate(const value_type &v, int len) { return v; } }; const pair Operate_structure::identity = make_pair(mat_id, vec_id); class Node { public: using value_structure = Value_structure; using operate_structure = Operate_structure; value_structure value; operate_structure op; private: using V = value_structure::value_type; using O = operate_structure::value_type; public: Node(V value, O op) : value(value), op(op) {} static const V operate(const V &l, const O &r) { return make_pair(r.first * l.first, r.first * l.second + r.second); } }; const double PI = acos(-1); int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); int n, q; cin >> n >> q; lazy_segtree st(n); cout << fixed << setprecision(10); auto get = [&](pair &p, int x, int y) -> pair { matrix init(2, 1, 0); init.v[0][0] = x; init.v[1][0] = y; auto m = p.first * init; m += p.second; return make_pair(m.v[0][0], m.v[1][0]); }; auto rot = [&](int l, int r, double theta) { vvd a(2, vd(2)), b(2, vd(1, 0)); a[0][0] = cos(theta); a[0][1] = -sin(theta); a[1][0] = sin(theta); a[1][1] = cos(theta); st.update(l, r, make_pair(mat(a), mat(b))); }; auto move = [&](int l, int r, double x, double y) { vvd a(2, vd(2, 0)), b(2, vd(1)); a[0][0] = 1; a[1][1] = 1; b[0][0] = x; b[1][0] = y; st.update(l, r, make_pair(mat(a), mat(b))); }; while (q--) { int t, i; cin >> t >> i; i--; if (t == 0) { int x; cin >> x; auto fl = st.fold(i, i + 1); auto[ox, oy] = get(fl, i + 1, 0); double bx = 0, by = 0; if (i > 0) { fl = st.fold(i - 1, i); tie(bx, by) = get(fl, i, 0); } move(i, n, -bx, -by); double theta = atan2(oy - by, ox - bx); if (i > 0) { double bbx = 0, bby = 0; if (i > 1) { fl = st.fold(i - 2, i - 1); tie(bbx, bby) = get(fl, i - 1, 0); } double btheta = atan2(by - bby, bx - bbx); theta -= btheta; } theta = (double) x * PI / double(180) - theta; rot(i, n, theta); move(i, n, bx, by); } else if (t == 1) { int x; cin >> x; auto fl = st.fold(i, i + 1); auto[ox, oy] = get(fl, i + 1, 0); double bx = 0, by = 0; if (i > 0) { fl = st.fold(i - 1, i); tie(bx, by) = get(fl, i, 0); } double d = (double) x / sqrt((ox - bx) * (ox - bx) + (oy - by) * (oy - by)); double nx = bx + (ox - bx) * d; double ny = by + (oy - by) * d; move(i, n, nx - ox, ny - oy); } else { auto fl = st.fold(i, i + 1); auto[x, y] = get(fl, i + 1, 0); cout << x << ' ' << y << endl; } } }