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 l i , a l i + 1, a l i + 2, ..., a r i . 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.

输入描述:

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.

输出描述:

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.