You've got an array, consisting of n integers a1,a2,...,an. Also, you've got m queries, the i-th query is described by two integers li,ri. Numbers li,ri define a subsegment of the original array, that is, the sequence of numbers ali,ali+1,ali+2,...,ari. For each query you should check whether the corresponding segment is a ladder.
A ladder is a sequence of integers b1,b2,...,bk, 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: b1≤b2≤...≤bx≥bx+1≥bx+2...≥bk. 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≤105) − the number of array elements and the number of queries. The second line contains the sequence of integers a1,a2,...,an (1≤ai≤109), where number ai 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 li, ri (1≤li≤ri≤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.
8 6
1 2 1 3 3 5 2 1
1 3
2 3
2 4
8 8
1 4
5 8
Yes
Yes
No
Yes
No
Yes