A11048 | Vladik and Complicated Book

Vladik had started reading a complicated book about algorithms containing $n$ pages. To improve understanding of what is written, his friends advised him to read pages in some order given by permutation $P=[p_{1},p_{2},...,p_{n}]$ , where $p_{i}$ denotes the number of page that should be read $i$ -th in turn.

Sometimes Vladik’s mom sorted some subsegment of permutation $P$ from position $l$ to position $r$ inclusive, because she loves the order. For every of such sorting Vladik knows number $x$ — what index of page in permutation he should read. He is wondered if the page, which he will read after sorting, has changed. In other words, has $p_{x}$ changed? After every sorting Vladik return permutation to initial state, so you can assume that each sorting is independent from each other.

First line contains two space-separated integers $n$ , $m$ ( $1<=n,m<=10^{4}$ ) — length of permutation and number of times Vladik's mom sorted some subsegment of the book.

Second line contains $n$ space-separated integers $p_{1},p_{2},...,p_{n}$ ( $1<=p_{i}<=n$ ) — permutation $P$ . Note that elements in permutation are distinct.

Each of the next $m$ lines contains three space-separated integers $l_{i}$ , $r_{i}$ , $x_{i}$ ( $1<=l_{i}<=x_{i}<=r_{i}<=n$ ) — left and right borders of sorted subsegment in $i$ -th sorting and position that is interesting to Vladik.

For each mom’s sorting on it’s own line print "Yes", if page which is interesting to Vladik hasn't changed, or "No" otherwise.