Codeforces Round 869 (Div. 1) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

binary search

data structures

greedy

*1500

No tag edit access

The problem statement has recently been changed. View the changes.

×
A. Almost Increasing Subsequence

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA sequence is almost-increasing if it does not contain three consecutive elements $$$x, y, z$$$ such that $$$x\ge y\ge z$$$.

You are given an array $$$a_1, a_2, \dots, a_n$$$ and $$$q$$$ queries.

Each query consists of two integers $$$1\le l\le r\le n$$$. For each query, find the length of the longest almost-increasing subsequence of the subarray $$$a_l, a_{l+1}, \dots, a_r$$$.

A subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements.

Input

The first line of input contains two integers, $$$n$$$ and $$$q$$$ ($$$1 \leq n, q \leq 200\,000$$$) — the length of the array $$$a$$$ and the number of queries.

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \leq a_i \leq 10^9$$$) — the values of the array $$$a$$$.

Each of the next $$$q$$$ lines contains the description of a query. Each line contains two integers $$$l$$$ and $$$r$$$ ($$$1 \leq l \leq r \leq n$$$) — the query is about the subarray $$$a_l, a_{l+1}, \dots, a_r$$$.

Output

For each of the $$$q$$$ queries, print a line containing the length of the longest almost-increasing subsequence of the subarray $$$a_l, a_{l+1}, \dots, a_r$$$.

Example

Input

9 8 1 2 4 3 3 5 6 2 1 1 3 1 4 2 5 6 6 3 7 7 8 1 8 8 8

Output

3 4 3 1 4 2 7 1

Note

In the first query, the subarray is $$$a_1, a_2, a_3 = [1,2,4]$$$. The whole subarray is almost-increasing, so the answer is $$$3$$$.

In the second query, the subarray is $$$a_1, a_2, a_3,a_4 = [1,2,4,3]$$$. The whole subarray is a almost-increasing, because there are no three consecutive elements such that $$$x \geq y \geq z$$$. So the answer is $$$4$$$.

In the third query, the subarray is $$$a_2, a_3, a_4, a_5 = [2, 4, 3, 3]$$$. The whole subarray is not almost-increasing, because the last three elements satisfy $$$4 \geq 3 \geq 3$$$. An almost-increasing subsequence of length $$$3$$$ can be found (for example taking $$$a_2,a_3,a_5 = [2,4,3]$$$ ). So the answer is $$$3$$$.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/15/2024 08:33:14 (g1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|