Non-overlapping Planting Sections

In a terrarium, there are designated sections occupied by plants. In this problem, you are given a list of sections, each represented as an interval $[L_i, R_i]$. You are also given a list of query intervals $[L_q, R_q]$. For each query interval, determine whether it is free of any overlap with the pre-defined sections. Two intervals $[L_i, R_i]$ and $[L_q, R_q]$ are said to overlap if they satisfy $$L_q \le R_i \quad\text{and}\quad R_q \ge L_i.$$

If a query interval does not overlap any existing section, output "Yes"; otherwise, output "No". All comparisons are inclusive. This problem tests your ability to perform interval comparisons and handle multiple queries efficiently.

inputFormat

The first line contains two integers $N$ and $Q$, where $N$ is the number of pre-defined sections and $Q$ is the number of queries. The next $N$ lines each contain two integers $L_i$ and $R_i$ representing the start and end points of the sections. This is followed by $Q$ lines, each containing two integers $L_q$ and $R_q$ for the query intervals.

outputFormat

For each query interval, output a single line containing either "Yes" if the interval does not overlap with any section, or "No" if it does.## sample

3 3
1 5
10 15
20 25
6 9
5 10
30 35

Yes
No
Yes