import bisect
from typing import List

class Solution:
    def __init__(self):
        self.bookings = []

    def book(self, nums: List[List[int]]) -> List[bool]:
        results = []

        for interval in nums:
            start, end = interval
            event = (start, end)
            
            # Find the index where the event should be inserted to maintain sorted order
            idx = bisect.bisect_left(self.bookings, event)

            # Find lower and higher neighbors
            lower = self.bookings[idx - 1] if idx > 0 else None
            higher = self.bookings[idx] if idx < len(self.bookings) else None

            # Check for overlap with neighboring events
            if (lower is None or lower[1] <= start) and (higher is None or end <= higher[0]):
                bisect.insort(self.bookings, event)  # Add to list if no overlap
                results.append(True)
            else:
                results.append(False)

        return results