A box office keeps a chronological log of the ticket prices charged for a long-running show, prices[0..n-1]. For an upcoming audit, the finance team wants to check several stretches of that log: for each stretch [l, r] (inclusive), they ask whether the prices charged during that stretch could be re-sorted into a perfect price ladder — a sequence where each step up costs exactly the same fixed amount more than the one before it (a constant difference between consecutive sorted prices; a difference of zero, i.e. every price in the stretch being identical, also counts as a valid ladder). For every query, report whether that stretch's prices can be arranged into such a ladder.

Input format

Line 1: two integers n q — the number of logged prices and the number of queries. Line 2: n integers — prices[0], prices[1], ..., prices[n-1]. Next q lines: each line has two integers l r (0-indexed, inclusive) describing one query stretch.

Output format

Print q lines. For the i-th query, print "YES" if prices[l..r] can be rearranged into a sequence with a constant difference between consecutive elements, otherwise print "NO".

Constraints

• 1 <= n <= 1000
• 1 <= q <= 1000
• 0 <= prices[i] <= 100000
• 0 <= l <= r <= n-1

6 2
10 14 12 20 8 16
0 2
0 3

YES
NO

4 1
5 5 5 5
1 3

YES