Day Streak

Recently Deltaforces, a famous competitive programming website, added a lot of new visual information to user profiles. In particular, there is a maximum day streak — the maximum number of days in a row with at least one problem solved. You decided that the maximum day streak in your profile does not accurately represent your training efforts. So you came up with a thought — what if you could change the time zone in your profile to increase the maximum day streak?

Let's formalize this setting as follows. Suppose you have solved $n$ problems, and the $i$-th problem was solved at time $a_i$. There are $m$ time zones, numbered from $0$ to $m-1$. The default time zone is $0$. If you decide to change your time zone to $t$, all solutions' timestamps increase by $t$: the problem solved at time $a_i$ is now considered to be solved at time $a_i+t$, for all $i$ simultaneously.

The problem solved at time $x$ is considered to be solved on day number $\lfloor \frac{x}{m}\rfloor$. Here $\lfloor v\rfloor$ means $v$ rounded down to the greatest integer less than or equal to $v$.

To display the maximum day streak, Deltaforces finds such $l$ and $r$ that you have solved at least one problem on each of days $l,l+1,\dots ,r$, and $r-l+1$ is as large as possible. Then your maximum day streak is shown as $r-l+1$.

Find the maximum day streak you can achieve by selecting a time zone.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1\le t\le 2\cdot 10^5$). Description of the test cases follows.

The first line of each test case contains two integers $n$ and $m$ — the number of solved problems and the number of time zones ($1\le n\le 2\cdot 10^5$; $1\le m\le 10^9$). The second line contains $n$ integers $a_1,a_2,\dots ,a_n$ — distinct timestamps of your solutions, in chronological order ($0\le a_1<a_2<\cdots <a_n\le 10^9$).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$.

Output

For each test case, print two integers $s$ and $t$ — the maximum day streak and any time zone that achieves it ($1\le s\le n$; $0\le t<m$).

Examples

Note

In the first example test case, when you select time zone $2$, the timestamps of your solutions change to $2$, $5$, $10$, and $26$. It means the problems are now considered to be solved on days $0$, $0$, $1$, and $2$; that is a $3$-day streak. Time zones $3$, $4$, and $5$ yield the same answer.

In the second example test case, timestamps of your solutions are $37$ and $40$ in time zone $5$, which corresponds to days $3$ and $4$. Time zones $6$ and $7$ also work.

In the third example test case, only one time zone exists, and your maximum day streak is $5$.

In the fourth example test case, you have solved many problems but in a short period of time, and you can't obtain more than a $2$-day streak.