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문제

Let’s call an array of integers $[b_1, b_2, \dots , b_m]$ good, if we can partition all of its elements into $2$ nonempty groups, such that the bitwise $\texttt{AND}$ of the elements in the first group is equal to the bitwise $\texttt{OR}$ of the elements in the second group. For example, the array $[1, 7, 3, 11]$ is good, as we can partition it into $[1, 3]$ and $[7, 11]$, where $1 \texttt{ OR } 3 = 3$, and $7\texttt{ AND }11 = 3$.

You are given an array $[a_1, a_2, \dots , a_n]$, and have to answer $q$ queries of form: is subarray $[a_l , a_{l+1}, \dots , a_r]$ good?

입력

The first line of the input contains two integer $n$, $q$ ($1 \le n \le 10^5$, $1 \le q \le 10^5$) — the length of the array and the number of the associated queries.

The second line of the input contains $n$ integers $a_1, a_2, \dots , a_n$ ($0 \le a_i \le 2^{30} - 1$) — the elements of the array.

The $i$-th of the next $q$ lines contains $2$ integers $l_i$, $r_i$ ($1 \le l_i \le r_i \le n$) — describing the $i$-th query.

출력

For each query, output YES, if the correspondent subarray is good, and NO, if it’s not.

예제 입력 1

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

예제 출력 1

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