Problem Statement

For sequences ~B=(B_1,B_2,\dots,B_M)~ and ~C=(C_1,C_2,\dots,C_M)~ , each of length ~M~ , consisting of non-negative integers, let the XOR sum ~S(B,C)~ of ~B~ and ~C~ be defined as the sequence ~(B_1\oplus C_1, B_2\oplus C_2, ..., B_{M}\oplus C_{M})~ of length ~M~ consisting of non-negative integers. Here, ~\oplus~ represents bitwise XOR.
For instance, if ~B = (1, 2, 3)~ and ~C = (3, 5, 7)~ , we have ~S(B, C) = (1\oplus 3, 2\oplus 5, 3\oplus 7) = (2, 7, 4)~ .

You are given a sequence ~A = (A_1, A_2, \dots, A_N)~ of non-negative integers. Let ~A(i, j)~ denote the contiguous subsequence composed of the ~i~ -th through ~j~ -th elements of ~A~ .
You will be given ~Q~ queries explained below and asked to process all of them.

Each query gives you integers ~a~ , ~b~ , ~c~ , ~d~ , ~e~ , and ~f~ , each between ~1~ and ~N~ , inclusive. These integers satisfy ~a \leq b~ , ~c \leq d~ , ~e \leq f~ , and ~b-a=d-c~ . If ~S(A(a, b), A(c, d))~ is strictly lexicographically smaller than ~A(e, f)~ , print Yes ; otherwise, print No .

What is bitwise XOR? The exclusive logical sum ~a \oplus b~ of two integers ~a~ and ~b~ is defined as follows.

• The ~2^k~ 's place ( ~k \geq 0~ ) in the binary notation of ~a \oplus b~ is ~1~ if exactly one of the ~2^k~ 's places in the binary notation of ~a~ and ~b~ is ~1~ ; otherwise, it is ~0~ .

For example, ~3 \oplus 5 = 6~ (In binary notation: ~011 \oplus 101 = 110~ ). What is lexicographical order on sequences?

A sequence ~A = (A_1, \ldots, A_{|A|})~ is said to be strictly lexicographically smaller than a sequence ~B = (B_1, \ldots, B_{|B|})~ if and only if 1. or 2. below is satisfied.

1. ~|A|<|B|~ and ~(A_{1},\ldots,A_{|A|}) = (B_1,\ldots,B_{|A|})~ .
2. There is an integer ~1\leq i\leq \min\\{|A|,|B|\\}~ that satisfies both of the following.
   • ~(A_{1},\ldots,A_{i-1}) = (B_1,\ldots,B_{i-1})~ .
   • ~A_i < B_i~ .

Constraints

• ~1 \leq N \leq 5 \times 10^5~
• ~0 \leq A_i \leq 10^{18}~
• ~1 \leq Q \leq 5 \times 10^4~
• ~1 \leq a \leq b \leq N~
• ~1 \leq c \leq d \leq N~
• ~1 \leq e \leq f \leq N~
• ~b - a = d - c~
• All values in the input are integers.

Input

The input is given from Standard Input in the following format, where ~\text{query}_i~ represents the ~i~ -th query:

~N~ ~Q~ ~A_1~ ~A_2~ ~\dots~ ~A_N~ ~\text{query}_1~ ~\text{query}_2~ ~\vdots~ ~\text{query}_Q~

The queries are in the following format:

~a~ ~b~ ~c~ ~d~ ~e~ ~f~

Output

Print ~Q~ lines. The ~i~ -th line should contain the answer to the ~i~ -th query.

Sample Input 1

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

Sample Output 1

No
No
Yes
No
Yes

For the first query, we have ~A(1, 3) = (1, 2, 3)~ and ~A(2, 4) = (2, 3, 1)~ , so ~S(A(1,3),A(2,4)) = (1 \oplus 2, 2 \oplus 3, 3 \oplus 1) = (3, 1, 2)~ . This is lexicographcially larger than ~A(1, 4) = (1, 2, 3, 1)~ , so the answer is No .
For the second query, we have ~S(A(1,2),A(2,3)) = (3, 1)~ and ~A(3,4) = (3, 1)~ , which are equal, so the answer is No .

Sample Input 2

10 10
725560240 9175925348 9627229768 7408031479 623321125 4845892509 8712345300 1026746010 4844359340 2169008582
5 6 5 6 2 6
5 6 1 2 1 1
3 8 3 8 1 6
5 10 1 6 1 7
3 4 1 2 5 5
7 10 4 7 2 3
3 6 1 4 7 9
4 5 3 4 8 9
2 6 1 5 5 8
4 8 1 5 1 9

Sample Output 2

Yes
Yes
Yes
Yes
No
No
No
No
No
No