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C. Ladder

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou'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.

Input

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.

Output

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.

Examples

Input

8 6

1 2 1 3 3 5 2 1

1 3

2 3

2 4

8 8

1 4

5 8

Output

Yes

Yes

No

Yes

No

Yes

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