Problem Description

An array $b$ is called a "good array" if and only if $b$ can be split into two non-empty subarrays such that the $\mathtt{OR}$ result of the first subarray is equal to the $\mathtt{AND}$ result of the second subarray. For example, for $\{1,7,3,11\}$, split it into $\{1,3\}$ and $\{7,11\}$. Then $1\ \mathtt{OR}\ 3 = 3$ and $7\ \mathtt{AND}\ 11 = 3$, so it is a good array.

Now you are given an array $a$ of length $n$ and $q$ queries. In each query, given $[l,r]$, determine whether $\{a_l, a_{l+1},\ldots,a_{r-1},a_{r}\}$ is a good array.

Input Format

The first line contains two integers $n\ (1 \leq n \leq 10^5)$ and $q\ (1 \leq q \leq 10^5)$.

The second line contains $n$ integers representing the sequence $a\ (0\leq a_i \leq 2^{30}-1)$.

The next $q$ lines each contain two integers $l,r\ (1 \leq l \leq r \leq n)$, representing a query.

Output Format

For each query, if the subarray is good, output YES; otherwise output NO.

5 15
0 1 1 3 2
1 1
1 2
1 3
1 4
1 5
2 2
2 3
2 4
2 5
3 3
3 4
3 5
4 4
4 5
5 5

NO
NO
YES
YES
YES
NO
YES
YES
YES
NO
NO
YES
NO
NO
NO

Hint

Translated by ChatGPT 5