Problem Statement

Given is a sequence of $N positive integers A = (A_1, \dots, A_N)$.
Process Q queries. In the $i-th query (1 \leq i \leq Q),$ determine whether it is possible to choose one or more elements from $A_{L_i}, A_{L_i + 1}, \dots, A_{R_i}$ so that their $\mathrm{XOR}$ is X_i.

What is $\mathrm{XOR}$?

The bitwise $\mathrm{XOR}$ of integers A and B, A\ $\mathrm{XOR}$\ B, is defined as follows:

• When A\ $\mathrm{XOR}$\ B is written in base two, the digit in the 2^k'$s place (k \geq 0)$ is 1 if exactly one of A and B is 1, and 0 otherwise.

For example, we have 3\ $\mathrm{XOR}$\ 5 = 6 (in base two: 011\ $\mathrm{XOR}$\ 101 = 110).

Input

Input is given from Standard Input in the following format:
N Q
$A_1 \ldots A_N$
L_1 R_1 X_1
$\vdots$
L_Q R_Q X_Q

Output

Print Q lines. The $i-th line (1 \leq i \leq Q)$ should contain Yes if it is possible to choose one or more elements from $A_{L_i}, A_{L_i + 1}, \dots, A_{R_i}$ so that their $\mathrm{XOR}$ is X_i, and No otherwise.

Constraints

• $1 \leq N \leq 4 \times 10^5$
• $1 \leq Q \leq 2 \times 10^5$
• $1 \leq A_i \lt 2^{60}$
• $1 \leq L_i \leq R_i \leq N$
• $1 \leq X_i \lt 2^{60}$
• All values in input are integers.

Sample Input 1

5 2
3 1 4 1 5
1 3 7
2 5 7

Sample Output 1

Yes
No

In the first query, you can choose A_1 and $A_3, whose \mathrm{XOR}$ is 7.
In the second query, there is no way to choose elements so that their $\mathrm{XOR}$ is 7.

Sample Input 2

10 10
8 45 56 9 38 28 33 5 15 19
10 10 53
3 8 60
1 10 29
5 7 62
3 7 51
8 8 52
1 4 60
6 8 32
4 8 58
5 9 2

Sample Output 2

No
No
Yes
No
Yes
No
No
No
Yes
Yes

见题面 Input 部分

见题面 Output 部分