# Sakurako's Birthday

Today is Sakurako's birthday, so you decided to make a good present. You think that the best present will be an array of $n$ equal integers. Unfortunately, you couldn't find such an array. But you are smart, so you can change any element in the array by exactly $k$. In other words, if you have an array $a$, you can choose integer $i$ ($1≤i≤n$) and replace $a_{i}$ with $a_{i}−k$ or $a_{i}+k$. You want to make Sakurako happy, so decide whether you can make an array to be of equal integers.

For example, if you found an array $[10,16,12,10,20]$ with $k=2$, you can make all elements equal to $12$. To do this, add $k$ to the first and fourth elements $(a_{1}+k=10+2=12)$, subtract $k$ from the second element two times $(s_{2}−2⋅k=16−2⋅2=12)$, don't change the third element and subtract $k$ from the last element four times ($a_{5}−4⋅k=20−4⋅2=12$).

## Input

The first line contains one integer $t$ ($1≤t≤10_{5}$) — the number of such arrays.

Each array is described in two lines.

The first line contains two integers $n$ and $k(1≤n≤2⋅10_{5};1≤k≤10_{9})$.

The second line contains $n$ integers $a_{1},…,a_{n}$ ($1≤a_{i}≤10_{9}$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2⋅10_{5}$.

## Output

For each array, output "`Yes`

" if Sakurako will be happy or "`No`

" otherwise.

## Examples

## Note

The first case was explained in the statement.

The second case has answer "`Yes`

", because you can make all numbers equal to $123$.

The third case has answer "`No`

", because it can be proven that the fifth element cannot be equal to any other element of the array after any number of operations.

## Scoring

($3$ points): $k=2$;

($8$ points): $a_{i}≤100$ for all arrays;

($18$ points): $n≤1000$ for all arrays; It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$.

($21$ points): without additional restrictions.