Problem Statement

You are given an integer sequence of length $N$, $A = (A_1, A_2, \\ldots, A_N)$, and a positive integer $K$.

For each $i = 1, 2, \\ldots, Q$, determine whether a contiguous subsequence of $A$, $(A_{l_i}, A_{l_i+1}, \\ldots, A_{r_i})$, is a good sequence.

Here, a sequence of length $n$, $X = (X_1, X_2, \\ldots, X_n)$, is good if and only if there is a way to perform the operation below some number of times (possibly zero) to make all elements of $X$ equal $0$.

Choose an integer $i$ such that $1 \\leq i \\leq n-K+1$ and an integer $c$ (possibly negative). Add $c$ to each of the $K$ elements $X_{i}, X_{i+1}, \\ldots, X_{i+K-1}$.

It is guaranteed that $r_i - l_i + 1 \\geq K$ for every $i = 1, 2, \\ldots, Q$.

Constraints

• $1 \\leq N \\leq 2 \\times 10^5$
• $1 \\leq K \\leq \\min\\lbrace 10, N \\rbrace$
• $\-10^9 \\leq A_i \\leq 10^9$
• $1 \\leq Q \\leq 2 \\times 10^5$
• $1 \\leq l_i, r_i \\leq N$
• $r_i-l_i+1 \\geq K$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $K$ $A_1$ $A_2$ $\\ldots$ $A_N$ $Q$ $l_1$ $r_1$ $l_2$ $r_2$ $\\vdots$ $l_Q$ $r_Q$

Output

Print $Q$ lines. For each $i = 1, 2, \\ldots, Q$, the $i$-th line should contain Yes if the sequence $(A_{l_i}, A_{l_i+1}, \\ldots, A_{r_i})$ is good, and No otherwise.

Sample Input 1

7 3
3 -1 1 -2 2 0 5
2
1 6
2 7

Sample Output 1

Yes
No

The sequence $X \\coloneqq (A_1, A_2, A_3, A_4, A_5, A_6) = (3, -1, 1, -2, 2, 0)$ is good. Indeed, you can do the following to make all elements equal $0$.

• First, do the operation with $i = 2, c = 4$, making $X = (3, 3, 5, 2, 2, 0)$.
• Next, do the operation with $i = 3, c = -2$, making $X = (3, 3, 3, 0, 0, 0)$.
• Finally, do the operation with $i = 1, c = -3$, making $X = (0, 0, 0, 0, 0, 0)$.

Thus, the first line should contain Yes.

On the other hand, for the sequence $(A_2, A_3, A_4, A_5, A_6, A_7) = (-1, 1, -2, 2, 0, 5)$, there is no way to make all elements equal $0$, so it is not a good sequence. Thus, the second line should contain No.

Sample Input 2

20 4
-19 -66 -99 16 18 33 32 28 26 11 12 0 -16 4 21 21 37 17 55 -19
5
13 16
4 11
3 12
13 18
4 10

Sample Output 2

No
Yes
No
Yes
No