Dominance Radius

Time limit: 2000 msMemory limit: 250 MB

You are given an array of integers $A_1, A_2, \ldots, A_N$ .

For each position $i$ with $1 \le i \le N$ , define its dominance radius $r_i$ as the largest integer $r$ such that all of the following hold:

$0 \le r \le \min(i - 1, N - i)$ ,
for every index $j$ with $i - r \leq j \leq$ and , the strict inequality holds.

You are given $Q$ independent queries. Each query provides an index $i$ and a non-negative integer $D$ . For each query, determine whether $r_i \ge D$ .

Input

The input consists of exactly $Q + 2$ lines.

Line 1: two integers $N$ and $Q$ separated by a single space, where $1 \le N \le 200000$ and .

Output

Output exactly $Q$ lines. For each query in input order:

Print the string "Yes" if $r_i \ge D$ .
Otherwise, print the string "No". Each line must contain exactly one of these words with the exact capitalization and no extra spaces.

Samples

Sample 1

Input

Output

Yes
No
Yes
No

For $N = 5$ and $A = [3, 1, 4, 1, 5]$ : the query $(i, D) = ($ asks whether is strictly greater than all values in except at , which is true, so the first line is "Yes". The other lines correspond to the remaining queries in order.

Dominance Radius

Input

Output

Samples

Sample 1

Submit

Submissions

Sample 2