A8931. Ladder

You've got an array, consisting of $n$ integers $a_{1},a_{2},...,a_{n}$ . Also, you've got $m$ queries, the $i$ -th query is described by two integers $l_{i},r_{i}$ . Numbers $l_{i},r_{i}$ define a subsegment of the original array, that is, the sequence of numbers $a_{li},a_{li}+1,a_{li}+2,...,a_{ri}$ . For each query you should check whether the corresponding segment is a ladder.

A ladder is a sequence of integers $b_{1},b_{2},...,b_{k}$ , such that it first doesn't decrease, then doesn't increase. In other words, there is such integer $x$ $(1<=x<=k)$ , that the following inequation fulfills: $b_{1}<=b_{2}<=...<=b_{x}>=b_{x+1}>=b_{x+2}...>=b_{k}$ . Note that the non-decreasing and the non-increasing sequences are also considered ladders.

The first line contains two integers $n$ and $m$ $(1<=n,m<=10^{5})$ — the number of array elements and the number of queries. The second line contains the sequence of integers $a_{1},a_{2},...,a_{n}$ $(1<=a_{i}<=10^{9}$ ), where number $a_{i}$ stands for the $i$ -th array element.

The following $m$ lines contain the description of the queries. The $i$ -th line contains the description of the $i$ -th query, consisting of two integers $l_{i}$ , $r_{i}$ $(1<=l_{i}<=r_{i}<=n)$ — the boundaries of the subsegment of the initial array.

The numbers in the lines are separated by single spaces.

Print $m$ lines, in the $i$ -th line print word "Yes" (without the quotes), if the subsegment that corresponds to the $i$ -th query is the ladder, or word "No" (without the quotes) otherwise.