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: $011\\ \\mathrm{XOR}\\ 101 = 110$).

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.

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.

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