class SegmentTree(): """UnitXは単位元、fは区間で行いたい操作、initは自然数あるいは配列""" def __init__(self, init, unitX, f): self.f = f # (X, X) -> X self.unitX = unitX self.f = f if type(init) == int: self.n = init self.n = 1 << (self.n - 1).bit_length() self.X = [unitX] * (self.n * 2) else: self.n = len(init) self.n = 1 << (self.n - 1).bit_length() # len(init)が2の累乗ではない時UnitXで埋める self.X = [unitX] * self.n + init + [unitX] * (self.n - len(init)) # 配列のindex1まで埋める for i in range(self.n-1, 0, -1): self.X[i] = self.f(self.X[i*2], self.X[i*2|1]) def update(self, i, x): """0-indexedのi番目の値をxで置換""" # 最下段に移動 i += self.n self.X[i] = x # 上向に更新 i >>= 1 while i: self.X[i] = self.f(self.X[i*2], self.X[i*2|1]) i >>= 1 def getvalue(self, i): """元の配列のindexの値を見る""" return self.X[i + self.n] def getrange(self, l, r): """区間[l, r)でのfを行った値""" l += self.n r += self.n al = self.unitX ar = self.unitX while l < r: # 左端が右子ノードであれば if l & 1: al = self.f(al, self.X[l]) l += 1 # 右端が右子ノードであれば if r & 1: r -= 1 ar = self.f(self.X[r], ar) l >>= 1 r >>= 1 return self.f(al, ar) # https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py import math from bisect import bisect_left, bisect_right, insort from typing import Generic, Iterable, Iterator, TypeVar, Union, List T = TypeVar('T') class SortedMultiset(Generic[T]): BUCKET_RATIO = 50 REBUILD_RATIO = 170 def _build(self, a=None) -> None: "Evenly divide `a` into buckets." if a is None: a = list(self) size = self.size = len(a) bucket_size = int(math.ceil(math.sqrt(size / self.BUCKET_RATIO))) self.a = [a[size * i // bucket_size : size * (i + 1) // bucket_size] for i in range(bucket_size)] def __init__(self, a: Iterable[T] = []) -> None: "Make a new SortedMultiset from iterable. / O(N) if sorted / O(N log N)" a = list(a) if not all(a[i] <= a[i + 1] for i in range(len(a) - 1)): a = sorted(a) self._build(a) def __iter__(self) -> Iterator[T]: for i in self.a: for j in i: yield j def __reversed__(self) -> Iterator[T]: for i in reversed(self.a): for j in reversed(i): yield j def __len__(self) -> int: return self.size def __repr__(self) -> str: return "SortedMultiset" + str(self.a) def __str__(self) -> str: s = str(list(self)) return "{" + s[1 : len(s) - 1] + "}" def _find_bucket(self, x: T) -> List[T]: "Find the bucket which should contain x. self must not be empty." for a in self.a: if x <= a[-1]: return a return a def __contains__(self, x: T) -> bool: if self.size == 0: return False a = self._find_bucket(x) i = bisect_left(a, x) return i != len(a) and a[i] == x def count(self, x: T) -> int: "Count the number of x." return self.index_right(x) - self.index(x) def add(self, x: T) -> None: "Add an element. / O(√N)" if self.size == 0: self.a = [[x]] self.size = 1 return a = self._find_bucket(x) insort(a, x) self.size += 1 if len(a) > len(self.a) * self.REBUILD_RATIO: self._build() def discard(self, x: T) -> bool: "Remove an element and return True if removed. / O(√N)" if self.size == 0: return False a = self._find_bucket(x) i = bisect_left(a, x) if i == len(a) or a[i] != x: return False a.pop(i) self.size -= 1 if len(a) == 0: self._build() return True def lt(self, x: T) -> Union[T, None]: "Find the largest element < x, or None if it doesn't exist." for a in reversed(self.a): if a[0] < x: return a[bisect_left(a, x) - 1] def le(self, x: T) -> Union[T, None]: "Find the largest element <= x, or None if it doesn't exist." for a in reversed(self.a): if a[0] <= x: return a[bisect_right(a, x) - 1] def gt(self, x: T) -> Union[T, None]: "Find the smallest element > x, or None if it doesn't exist." for a in self.a: if a[-1] > x: return a[bisect_right(a, x)] def ge(self, x: T) -> Union[T, None]: "Find the smallest element >= x, or None if it doesn't exist." for a in self.a: if a[-1] >= x: return a[bisect_left(a, x)] def __getitem__(self, x: int) -> T: "Return the x-th element, or IndexError if it doesn't exist." if x < 0: x += self.size if x < 0: raise IndexError for a in self.a: if x < len(a): return a[x] x -= len(a) raise IndexError def index(self, x: T) -> int: "Count the number of elements < x." ans = 0 for a in self.a: if a[-1] >= x: return ans + bisect_left(a, x) ans += len(a) return ans def index_right(self, x: T) -> int: "Count the number of elements <= x." ans = 0 for a in self.a: if a[-1] > x: return ans + bisect_right(a, x) ans += len(a) return ans N, Q = map(int, input().split()) q1 = [] q2 = [list() for _ in range(N+1)] for i in range(Q): l,r,b = list(map(int, input().split())) q2[l-1].append([1,b]) q2[r].append([2,b]) q1.append([l-1,r,b]) res = [10**9]*N sm = SortedMultiset() for i in range(N): for t, b in q2[i]: if t==1: sm.add(b) else: sm.discard(b) l = len(sm) if l==0:continue res[i] = sm[len(sm)-1] st = SegmentTree(res,10**9,min) for l, r, b in q1: if st.getrange(l,r)!=b: exit(print(-1)) print(*res)