Curtains

Benson the Rabbit is organizing a performance on his plane!

He has a stage with $n$ sections numbered $1$ to $n$ from left to right. He also has $m$ curtains numbered from $1$ to $m$.

Each of these $m$ curtains can be lowered. Lowering curtain $i$ covers sections $l\[i]$ to $r\[i]$. A curtain configuration is a set of lowered curtains. Given a curtain configuration, a section $x$ ($1 ≤ x ≤ n$) is covered if and only if there exists a lowered curtain $i$ such that $l\[i] ≤ x ≤ r\[i]$.

Benson wants to give a total of $q$ performances, numbered from $1$ to $q$. For each performance $j$, Benson requires a curtain configuration such that the sections $s\[j]$ to $e\[j]$ are covered and nothing else is covered. More formally, for each $1 ≤ x ≤ n$,

• If $s\[j] ≤ x ≤ e\[j]$, section $x$ is covered.
• Otherwise, section $x$ is not covered.

For each of these $q$ performances, help Benson to determine if there exists a curtain configuration satisfying his requirements.

The first line of input will contain $3$ spaced integers $n$, $m$ and $q$, representing the number of sections, curtains and performances respectively.

The next $m$ lines of input will contain $2$ spaced integers each. The $i$-th of these lines will contain $l\[i]$ and $r\[i]$ respectively, describing the range of sections that curtain $i$ can cover.

The next $q$ lines of input will contain $2$ spaced integers each. The $j$-th of these lines will contain $s\[j]$ and $e\[j]$ respectively, describing the range of sections that need to be covered for performance $j$.

Output $q$ lines, the $j$-th of which should contain YES if it is possible to cover the required sections for the $j$-th performance using the curtains, and NO otherwise.

• $1 ≤ n, m, q ≤ 500\\,000$
• $1 ≤ l\[i] ≤ r\[i] ≤ n$ (for all $1 ≤ i ≤ m$)
• $1 ≤ s\[j] ≤ e\[j] ≤ n$ (for all $1 ≤ j ≤ q$)