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. 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.