Level Up
Description
Monocarp is playing a computer game. He starts the game being level $1$. He is about to fight $n$ monsters, in order from $1$ to $n$. The level of the $i$-th monster is $a_i$.
For each monster in the given order, Monocarp's encounter goes as follows:
- if Monocarp's level is strictly higher than the monster's level, the monster flees (runs away);
- otherwise, Monocarp fights the monster.
After every $k$-th fight with a monster (fleeing monsters do not count), Monocarp's level increases by $1$. So, his level becomes $2$ after $k$ monsters he fights, $3$ after $2k$ monsters, $4$ after $3k$ monsters, and so on.
You need to process $q$ queries of the following form:
- $i~x$: will Monocarp fight the $i$-th monster (or will this monster flee) if the parameter $k$ is equal to $x$?
The first line contains two integers $n$ and $q$ ($1 \le n, q \le 2 \cdot 10^5$) — the number of monsters and the number of queries.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 2 \cdot 10^5$) — the levels of the monsters.
In the $j$-th of the following $q$ lines, two integers $i$ and $x$ ($1 \le i, x \le n$) — the index of the monster and the number of fights required for a level up in the $j$-th query.
For each query, output "YES", if Monocarp will fight the $i$-th monster in this query, and "NO", if the $i$-th monster flees.
Input
The first line contains two integers $n$ and $q$ ($1 \le n, q \le 2 \cdot 10^5$) — the number of monsters and the number of queries.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 2 \cdot 10^5$) — the levels of the monsters.
In the $j$-th of the following $q$ lines, two integers $i$ and $x$ ($1 \le i, x \le n$) — the index of the monster and the number of fights required for a level up in the $j$-th query.
Output
For each query, output "YES", if Monocarp will fight the $i$-th monster in this query, and "NO", if the $i$-th monster flees.
4 16
2 1 2 1
1 1
2 1
3 1
4 1
1 2
2 2
3 2
4 2
1 3
2 3
3 3
4 3
1 4
2 4
3 4
4 4
7 15
1 1 2 1 1 1 1
5 3
2 2
2 2
1 6
5 1
5 5
7 7
3 5
7 4
4 3
2 5
1 2
5 6
4 1
6 1
YES
NO
YES
NO
YES
YES
YES
NO
YES
YES
YES
NO
YES
YES
YES
YES
NO
YES
YES
YES
NO
YES
YES
YES
NO
NO
YES
YES
YES
NO
NO