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 $x$?

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.

见题面 Input 部分

见题面 Output 部分