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 $i = 1, 2, \ldots, Q$.

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.

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.

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

见题面 Input 部分

见题面 Output 部分