import sys input = lambda: sys.stdin.readline().rstrip() class SegmentTree(): def __init__(self, init, unitX, unitA, f, g, h): self.f = f # (X, X) -> X self.g = g # (X, A, size) -> X self.h = h # (A, A) -> A self.unitX = unitX self.unitA = unitA self.f = f if type(init) == int: self.n = init # self.n = 1 << (self.n - 1).bit_length() self.X = [unitX] * (self.n * 2) self.size = [1] * (self.n * 2) else: self.n = len(init) # self.n = 1 << (self.n - 1).bit_length() self.X = [unitX] * self.n + init + [unitX] * (self.n - len(init)) self.size = [0] * self.n + [1] * len(init) + [0] * (self.n - len(init)) for i in range(self.n-1, 0, -1): self.X[i] = self.f(self.X[i*2], self.X[i*2|1]) for i in range(self.n - 1, 0, -1): self.size[i] = self.size[i*2] + self.size[i*2|1] self.A = [unitA] * (self.n * 2) def update(self, i, x): i += self.n self.propagate_above(i) self.X[i] = x self.A[i] = unitA self.calc_above(i) def calc(self, i): return self.g(self.X[i], self.A[i], self.size[i]) def calc_above(self, i): i >>= 1 while i: self.X[i] = self.f(self.calc(i*2), self.calc(i*2|1)) i >>= 1 def propagate(self, i): self.X[i] = self.g(self.X[i], self.A[i], self.size[i]) self.A[i*2] = self.h(self.A[i*2], self.A[i]) self.A[i*2|1] = self.h(self.A[i*2|1], self.A[i]) self.A[i] = self.unitA def propagate_above(self, i): H = i.bit_length() for h in range(H, 0, -1): self.propagate(i >> h) def propagate_all(self): for i in range(1, self.n): self.propagate(i) def getrange(self, l, r): l += self.n r += self.n l0, r0 = l // (l & -l), r // (r & -r) - 1 self.propagate_above(l0) self.propagate_above(r0) al = self.unitX ar = self.unitX while l < r: if l & 1: al = self.f(al, self.calc(l)) l += 1 if r & 1: r -= 1 ar = self.f(self.calc(r), ar) l >>= 1 r >>= 1 return self.f(al, ar) def getvalue(self, i): i += self.n self.propagate_above(i) return self.calc(i) def operate_range(self, l, r, a): l += self.n r += self.n l0, r0 = l // (l & -l), r // (r & -r) - 1 self.propagate_above(l0) self.propagate_above(r0) while l < r: if l & 1: self.A[l] = self.h(self.A[l], a) l += 1 if r & 1: r -= 1 self.A[r] = self.h(self.A[r], a) l >>= 1 r >>= 1 self.calc_above(l0) self.calc_above(r0) def check(self, randX, randA, maxs = 20): from random import randrange for i in range(10000): x = randX() y = randX() z = randX() a = randA() b = randA() c = randA() s = randrange(1, maxs + 1) t = randrange(1, maxs + 1) err = 0 if not f(x, unitX) == f(unitX, x) == x: err = 1 print("!!!!! unitX Error !!!!!") print("unitX =", unitX) print("x =", x) print("f(x, unitX) =", f(x, unitX)) print("f(unitX, x) =", f(unitX, x)) if not h(a, unitA) == h(unitA, a) == a: err = 1 print("!!!!! unitA Error !!!!!") print("unitA =", unitA) print("a =", a) print("f(a, unitA) =", f(a, unitA)) print("f(unitA, a) =", f(unitA, a)) if not f(f(x, y), z) == f(x, f(y, z)): err = 1 print("!!!!! Associativity Error X !!!!!") print("x, y, z, f(x, y), f(y, x) =", x, y, z, f(x, y), f(y, x)) print("f(f(x, y), z) =", f(f(x, y), z)) print("f(x, f(y, z)) =", f(x, f(y, z))) if not h(h(a, b), c) == h(a, h(b, c)): err = 1 print("!!!!! Associativity Error A !!!!!") print("a, b, c, h(a, b), h(b, c) =", a, b, c, h(a, b), h(b, c)) print("h(h(a, b), c) =", h(h(a, b), c)) print("h(a, h(b, c)) =", h(a, h(b, c))) if not g(x, unitA, s) == x: err = 1 print("!!!!! Identity Error !!!!!") print("unitA, x, s =", unitA, x, s) print("g(x, unitA, s) =", g(x, unitA, s)) if not g(g(x, a, s), b, s) == g(x, h(a, b), s): err = 1 print("!!!!! Act Error 1 !!!!!") print("x, a, b, s, g(x, a, s), h(a, b) =", x, a, b, s, g(x, a, s), h(a, b)) print("g(g(x, a, s), b, s) =", g(g(x, a, s), b, s)) print("g(x, h(a, b), s) =", g(x, h(a, b), s)) if not g(f(x, y), a, s + t) == f(g(x, a, s), g(y, a, t)): err = 1 print("!!!!! Act Error 2 !!!!!") print("x, y, a, s, t, f(x, y), g(x, a, s), g(y, a, t) =", x, y, a, s, t, f(x, y), g(x, a, s), g(y, a, t)) print("g(f(x, y), a, s + t) =", g(f(x, y), a, s + t)) print("f(g(x, a, s), g(y, a, t)) =", f(g(x, a, s), g(y, a, t))) if err: break assert f(x, unitX) == f(unitX, x) == x assert h(a, unitA) == h(unitA, a) == a assert f(f(x, y), z) == f(x, f(y, z)) assert h(h(a, b), c) == h(a, h(b, c)) assert g(x, unitA, s) == x assert g(g(x, a, s), b, s) == g(x, h(a, b), s) assert g(f(x, y), a, s + t) == f(g(x, a, s), g(y, a, t)) else: pass # print("Monoid Check OK!") def debug1(self): print("self.n =", self.n) deX = [] deA = [] deS = [] a, b = self.n, self.n * 2 while b: deX.append(self.X[a:b]) deA.append(self.A[a:b]) deS.append(self.size[a:b]) a, b = a//2, a print("--- debug ---") for d in deX[::-1]: print(d) print("--- ---") for d in deA[::-1]: print(d) print("--- ---") for d in deS[::-1]: print(d) print("--- ---") def debug(self, k = 10): print("--- debug ---") print("point") for i in range(min(self.n - 1, k)): print(i, self.getvalue(i)) print("prod") for i in range(min(self.n, k)): print(i, self.getrange(0, i)) print("--- ---") from math import tan, sin, cos, pi, sqrt, atan2 f = lambda x, y: (x[0] + y[0], x[1] + y[1]) g = lambda x, a, s: (a[0] * x[0] - a[1] * x[1], a[1] * x[0] + a[0] * x[1]) h = lambda a, b: (a[0] * b[0] - a[1] * b[1], a[0] * b[1] + a[1] * b[0]) unitA = (1, 0) # * (a + bi), + (c + di) unitX = (0, 0) # x, y z = pi / 180 N, Q = map(int, input().split()) st = SegmentTree([(1, 0) for _ in range(N)], unitX, unitA, f, g, h) if True: from random import randrange randX = lambda: (randrange(-10, 11), randrange(-10, 11)) randA = lambda: (randrange(-10, 11), randrange(-10, 11)) maxs = 10 st.check(randX, randA, maxs) for _ in range(Q): q = [int(a) for a in input().split()] if q[0] == 0: i, s = q[1:] s *= z i -= 1 x, y = st.getvalue(i) r = sqrt(x**2 + y**2) t = atan2(y, x) if i == 0: u = 0 else: x2, y2 = st.getvalue(i-1) u = atan2(y2, x2) st.operate_range(i, N, (cos((s - t + u)), sin((s - t + u)))) elif q[0] == 1: i, s = q[1:] i -= 1 x, y = st.getvalue(i) r = sqrt(x**2 + y**2) x *= s / r y *= s / r st.update(i, (x, y)) else: i = q[1] print(*st.getrange(0, i))