Problem Statement

You are given $T$ test cases. Solve the following problem for each of them.

You keep $N$ slimes.

The slimes are lined up in a row, and the health of the $i$-th slime from the left is $H_i$.

You can cast the following healing magic any number of times.

• Choose any $K$ consecutive slimes and increase their health by $X$.

You do not like only some of the slimes having low health, so you want to make the health of all slimes the same.

Determine whether it is possible to make the health of all slimes the same.

Constraints

• $1 \leq T \leq 10^{5}$
• $2 \leq N \leq 2 \times 10^{5}$
• $1 \leq K \leq N$
• $1 \leq X \leq 10^{9}$
• $1 \leq H_i \leq 10^{9}$
• For the test cases contained in $1$ input, the sum of $N$ is at most $2 \times 10^{5}$.
• All input values are integers.

Input

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

$T$
$\text{case}_1$
$\vdots$

$\text{case}_T$

Each test case is given in the following format.

$N$ $K$ $X$ 
$H_1$ $H_2$ ... $H_{N}$ 

Output

Print $T$ lines. On the $i$-th line, for the $i$-th test case, print Yes if it is possible to make the health of all slimes the same, and No if it is impossible.

Sample

4
4 2 3
5 2 5 8
8 3 4
17 5 5 21 29 17 21 25
4 3 8
2 3 5 7
3 2 1
7 7 7

Yes
Yes
No
Yes