Alternating Heights

Troy is planning to take a group photo of the students at CCO and has asked you for help.

There are $K$ students, numbered from $1$ to $K$. Troy has forgotten the students' heights but remembers that no two students have the same height.

Troy has prepared a sequence $A\_1, A\_2, \ldots, A\_N$ representing the order of students in the group photo, from left to right. It is possible for a student to appear multiple times in $A$. You aren't sure how this group photo would be taken, but you're unwilling to assume that Troy made a mistake.

Troy will ask you $Q$ queries of the form x y, which is a compact way of asking "Given the sequence of students, $A\_x, A\_{x + 1}, \dots, A\_y$, can their heights form an alternating sequence?" More precisely, we denote the height of the $i^\text{th}$ student as $h\[i]$. If there exists an assignment of heights $h\[1], h\[2], \ldots, h\[K]$ such that $h\[A\_x] > h\[A\_{x + 1}] < h\[A\_{x + 2}] > h\[A\_{x + 3}] < \ldots h\[A\_y]$, answer YES; otherwise, answer NO.

Note that each of the $Q$ queries will be independent: that is, the assignment of heights for query $i$ is independent of the assignment of heights for query $j$ so long as $i \ne j$.

The first line of input will contain three space-separated integers $N$, $K$, and $Q$.

The second line of input will contain the array $A\_1, A\_2, \ldots, A\_N$ $(1 \le A\_i \le K)$.

The next $Q$ lines will each contain a query of the form of two space-separated integers $x$ and $y$ $(1 \le x < y \le N)$.

Output $Q$ lines. On the $i^\text{th}$ line, output the answer to Troy's $i^\text{th}$ query. Note that the answer is either YES or NO.

For the first query, we will never have $h\[1] > h\[1]$, so the answer is no.

For the second query, one solution to $h\[1] > h\[2] < h\[3] > h\[1]$ is $h\[1] = 160cm, h\[2] = 140cm, h\[3] = 180cm$. Another solution could be $h\[1] = 1.55m, h\[2] = 1.473m, h\[3] = 1.81m$.

For the third query, we cannot have both $h\[1] > h\[2]$ and $h\[1] < h\[2]$.