// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define double ld #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define rep1(i,n) for (int i = 1; i <= (int)(n); i++) #define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i,n) for (int i = (int)(n); i >= 1; i--) #define loop(i,a,B) for (int i = a; i B; i++) #define loopR(i,a,B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define pb push_back #define eb emplace_back #define mp make_pair #define fst first #define snd second template auto constexpr inf = numeric_limits::max()/2-1; auto constexpr INF32 = inf; auto constexpr INF64 = inf; auto constexpr INF = inf; #ifdef LOCAL #include "debug.hpp" #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template using pque_max = priority_queue; template using pque_min = priority_queue, greater >; template ::value>::type> ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; } template ::value>::type> istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << "(" << p.first << ", " << p.second << ")"; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; } template constexpr auto sumof(It b, It e) { using S = typename iterator_traits::value_type; using T = conditional_t,i64,u64>; return accumulate(b,e,T{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(v.begin(), v.end(), x)-v.begin(); } template int ubd(C const& v, T const& x) { return upper_bound(v.begin(), v.end(), x)-v.begin(); } const int dx[] = { 1,0,-1,0 }; const int dy[] = { 0,1,0,-1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } template Int rand(Int a, Int b) { // [a,b] static mt19937_64 mt{random_device{}()}; return uniform_int_distribution(a,b)(mt); } i64 irand(i64 a, i64 b) { return rand(a,b); } u64 urand(u64 a, u64 b) { return rand(a,b); } // <<< using Real = double; constexpr Real eps = 1e-10; constexpr Real pi = acos(-1.0L); constexpr Real to_rad(int deg) { return Real(deg) * pi / 180; } constexpr Real to_deg(Real rad) { return rad * 180 / pi; } template constexpr T sq(T const& x) { return x*x; } constexpr int sgn(Real x) { return x > eps ? 1 : x < -eps ? -1 : 0; } constexpr int sgn(int x) { return x > 0 ? 1 : x < 0 ? -1 : 0; } // >>> Point template struct Point { T x,y; constexpr Point(T x = 0, T y = 0) : x(x), y(y) {} constexpr pair to_pair() const { return {x,y}; } constexpr Point inv() const { return {x/norm(),-y/norm()}; } constexpr Point conj() const { return {x,-y}; } constexpr T norm() const { return x*x + y*y; } constexpr Point rot90(int n = 1) const { n %= 4; if (n < 0) n += 4; if (n == 1) return *this * Point(0,1); if (n == 2) return *this * (-1); if (n == 3) return *this * Point(0,-1); return *this; } constexpr Point operator+() const { return *this; } constexpr Point operator-() const { return {-x,-y}; } constexpr Point operator+(Point const& p) const { return {x+p.x, y+p.y}; } constexpr Point operator-(Point const& p) const { return {x-p.x, y-p.y}; } constexpr Point operator*(Point const& p) const { return {x*p.x-y*p.y, x*p.y+y*p.x}; } constexpr Point operator/(Point const& p) const { return *this * p.inv(); } constexpr Point& operator+=(Point const& p) { return *this = *this + p; } constexpr Point& operator-=(Point const& p) { return *this = *this - p; } constexpr Point& operator*=(Point const& p) { return *this = *this * p; } constexpr Point& operator/=(Point const& p) { return *this = *this / p; } constexpr friend Point operator*(T const& a, Point const& p) { return Point(a)*p; } constexpr friend Point operator/(T const& a, Point const& p) { return Point(a)/p; } constexpr T dot(Point const& q) const { return x*q.x + y*q.y; } constexpr T cross(Point const& q) const { return x*q.y - y*q.x; } constexpr T dot(Point const& p, Point const& q) const { return dot(p-*this,q-*this); } constexpr T cross(Point const& p, Point const& q) const { return cross(p-*this,q-*this); } constexpr bool operator==(Point const& q) const { return sgn(x-q.x) == 0 && sgn(y-q.y) == 0; } constexpr bool operator!=(Point const& q) const { return !operator==(q); } constexpr friend Point conj(Point const& p) { return p.conj(); } constexpr friend T norm(Point const& p) { return p.x*p.x + p.y*p.y; } constexpr friend T dot(Point const& p, Point const& q) { return p.dot(q); } constexpr friend T cross(Point const& p, Point const& q) { return p.cross(q); } #ifdef LOCAL friend string to_s(Point const& p) { return to_s(p.to_pair()); } #endif friend istream& operator>>(istream& is, Point& p) { return is >> p.x >> p.y; } }; // <<< template constexpr Real abs(Point const& p) { return sqrt((Real)p.norm()); } constexpr Point normalize(Point const& p) { return p/abs(p); } using P = Point; // >>> lazy segment tree template struct LazySegtree : Handler { static int32_t btmbit(int64_t x) { return x ? __builtin_ctzll(x) : -1; } // static int32_t btmbit(int32_t x) { return x ? __builtin_ctz(x) : -1; } using Value = typename Handler::Value; using Lazy = typename Handler::Lazy; using Handler::unit_value; // () -> Value using Handler::unit_action; // () -> Lazy using Handler::merge; // (Value,Value) -> Value using Handler::act; // (Lazy,Lazy&,Value&) -> void vector v; vector lz; int n; mutable Lazy tmp; LazySegtree() {} template LazySegtree(T&&... x) { init(forward(x)...); } template ()(0))> void init(int n, F gen) { assert(n >= 0); this->n = n; v.resize(2*n); lz.assign(n, unit_action()); for (int i = 0; i < n; i++) v[n+i] = gen(i); for (int i = n-1; i >= 1; i--) v[i] = merge(v[2*i],v[2*i+1]); } void init(int n) { init(n, [&](int) { return unit_value(); }); } void init(int n, Value const& x) { init(n, [&](int) { return x; }); } void init(vector const& v) { init(v.size(), [&](int i) { return v[i]; }); } int size() const { return n; } void act(Lazy const& x, int i) { act(x, (i < n ? lz[i] : tmp), v[i]); } void flush(int k) { if (n <= k || lz[k] == unit_action()) return; act(lz[k], 2*k); act(lz[k], 2*k+1); lz[k] = unit_action(); } void flush(int l, int r) { for (int p = __lg(l += n), q = __lg(r += n-1); q; --p,--q) { flush(l >> p); flush(r >> q); } } void build(int i) { i += n; i >>= btmbit(i); while (i >>= 1) v[i] = merge(v[2*i],v[2*i+1]); } Value get(int l, int r) { assert(0 <= l); assert(l <= r); assert(r <= n); flush(l,r); Value x = unit_value(), y = unit_value(); for (l += n, r += n; l < r; l >>= 1, r >>= 1) { if (l&1) x = merge(x,v[l++]); if (r&1) y = merge(v[--r],y); } return merge(x,y); } void apply(int l, int r, Lazy const& x) { assert(0 <= l); assert(l <= r); assert(r <= n); flush(l,r); for (int a = l+n, b = r+n; a < b; a >>= 1, b >>= 1) { if (a&1) act(x, a++); if (b&1) act(x, --b); } build(l); build(r); } Value operator[](int i) const { return get(i); } Value get(int i) const { assert(0 <= i); assert(i < n); Value x = v[i += n]; while (i >>= 1) act(lz[i], tmp, x); return x; } void set(int i, Value const& x) { assert(0 <= i); assert(i < n); for (int p = __lg(i += n); p; --p) flush(i >> p); for (v[i] = x; i >>= 1; ) v[i] = merge(v[2*i],v[2*i+1]); } vector dat() const { vector ret(size()); for (int i = 0; i < size(); i++) ret[i] = get(i); return ret; } }; // <<< struct H { using Value = P; using Lazy = P; constexpr static Value unit_value() { return 0; } constexpr static Lazy unit_action() { return 1; } constexpr static Value merge(Value const& x, Value const& y) { return x+y; } static void act(Lazy x, Lazy &y, Value &z) { y *= x, z *= x; } }; // >>> BIT struct BIT { int n; vector v; // use v[1..n] BIT(int n = 0) : n(n), v(n+1) {} int size() const { return n; } int get(int i) const { return sum(i+1)-sum(i); } void set(int i, int x) { add(i,x-get(i)); } void add(int i, int x) { assert(0 <= i); assert(i < n); for (i++; i <= n; i += i&(-i)) v[i] += x; } int sum(int r) const { // [0,r) assert(0 <= r); assert(r <= n); int s = 0; for (int i = r; i > 0; i -= i&(-i)) s += v[i]; return s; } int sum(int l, int r) const { // [l,r) return sum(r)-sum(l); } // lower_bound({sum(0),sum(1),...,sum(n)}, x) int lower_bound(int x) const { if (x <= 0) return 0; int s = 0, i = 0, w = 1; while (2*w <= n) w *= 2; for ( ; w; w >>= 1) { if (i+w <= n && s+v[i+w] < x) { s += v[i+w]; i += w; } } return i+1; } int upper_bound(int x) const { int s = 0, i = 0, w = 1; while (2*w <= n) w *= 2; for ( ; w; w >>= 1) { if (i+w <= n && s+v[i+w] <= x) { s += v[i+w]; i += w; } } return i+1; } }; // <<< ll mod(ll x, ll m) { return (x %= m) < 0 ? x+m : x; } int32_t main() { int n,q; cin >> n >> q; vector

tab(360); rep (i,360) tab[i] = {cosl(to_rad(i)),sinl(to_rad(i))}; BIT theta(n); LazySegtree seg(n,1); rep (_,q) { int t,i; cin >> t >> i; --i; if (t == 0) { int x; cin >> x; int old = theta.get(i); theta.set(i,x); seg.apply(i,n,tab[mod(x-old,360)]); } if (t == 1) { int x; cin >> x; int angle = theta.sum(i+1); seg.set(i,tab[mod(angle,360)]*x); } if (t == 2) { auto [x,y] = seg.get(0,i+1); cout << x << " " << y << "\n"; } } }