### 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.

Yes
No

The sequence $X:=(A_1,A_2,A_3,A_4,A_5,A_6)=(3,−1,1,−2,2,0)$ 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 00, so it is not a good sequence. Thus, the second line should contain No.