You have been gifted a magic sequence of integers: $a_1, a_2, \ldots, a_n$. However, this is no ordinary sequence — it can modify itself in a specific way!

After observing it carefully, you discovered the rule it follows:

• Repeatedly, two indices $1 \le i \le j \le n$ are chosen.
• Then, the value at index $j$ is updated as: $a_j \leftarrow a_j \oplus a_i$.$^{\text{∗}}$

Being afraid of strictly increasing sequences, you start asking yourself questions:

You are given $q$ queries. Each query consists of two integers $l$ and $r$, and you must determine whether the subarray $a_l, a_{l+1}, \ldots, a_r$ can be transformed into a strictly increasing sequence by applying any number of the described operations only within the range $l$ to $r$, that is, only using indices $l \le i \le j \le r$.

$^{\text{∗}}$$\oplus$ denotes the bitwise XOR operation.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line contains two integers $n$ and $q$ ($1 \leq n, q \leq 2 \cdot 10^5$) — the length of the sequence and the number of queries.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \lt 2^{20}$) — the contents of the sequence.

Each of the next $q$ lines contains two integers $l$ and $r$ ($1 \leq l \leq r \leq n$), representing a query. For each query, you must determine whether the subarray $a_l, a_{l+1}, \ldots, a_r$ can be transformed into a strictly increasing sequence using the allowed operations.

It is guaranteed that the total sum of $n$ over all test cases does not exceed $2 \cdot 10^5$, and the total sum of $q$ over all test cases does not exceed $2 \cdot 10^5$.

Output

For each query, output YES if the subarray $a_l, a_{l+1}, \ldots, a_r$ can be transformed into a strictly increasing sequence using the allowed operations; otherwise, output NO.

You may print each letter of YES or NO in any case. For example, YES, yES, YeS will all be recognized as a positive answer.

Note

In the first test case:

For the first query, the sequence is $[1]$, which is increasing, so no changes are needed.

For the second query, the sequence is $[1, 2]$, which is also increasing, no changes required.

For the third query the seqeunce is $[1, 2, 2]$ which is not strictly increasing so we have to make some operations. If we apply $i = 1, j = 3$ then $a_3 \leftarrow a_3 \oplus a_1$. The sequence becomes $[1, 2, 3]$ which is now strictly increasing. Thus, the answer is positive.

For the fourth query the sequence is $[1, 2, 2, 1]$. We can do the following:

1. $a_2 \leftarrow a_2 \oplus a_2 (i = 2, j = 2)$. The seqeuence becomes $[1, 0, 2, 1]$.
2. $a_4 \leftarrow a_4 \oplus a_3 (i = 3, j = 4)$. The sequence becomes $[1, 0, 2, 3]$.
3. $a_2 \leftarrow a_2 \oplus a_1 (i = 1, j = 2)$. The sequence becomes $[1, 1, 2, 3]$.
4. $a_1 \leftarrow a_1 \oplus a_1 (i = 1, j = 1)$. The sequence becomes $[0, 1, 2, 3]$ which is strictly increasing.

In the second test case:

For the first query, it is not possible to make the entire sequence strictly increasing.

For the second query, the sequence is $[1]$, which is already strictly increasing, so no changes are needed.

In the third query, the sequence is $[1, 1]$. We can make it strictly increasing by choosing $i = j = 2$ (referring to the indices in the original sequence) and performing the operation $a_2 \leftarrow a_2 \oplus a_2$. This sets $a_2 = 0$, resulting in the subarray from index 2 to 3 becoming $[0, 1]$, which is strictly increasing.

For the final query, we can perform the following operations in this order:

1. $a_6 \leftarrow a_6 \oplus a_5$
2. $a_7 \leftarrow a_7 \oplus a_5$
3. $a_5 \leftarrow a_5 \oplus a_5$

After these operations, the subarray from index 5 to 8 becomes $[0, 1, 2, 3]$, which is strictly increasing.