Array Beauty
Description
Let's call beauty of an array $b_1, b_2, \ldots, b_n$ ($n > 1$) — $\min\limits_{1 \leq i < j \leq n} |b_i - b_j|$.
You're given an array $a_1, a_2, \ldots a_n$ and a number $k$. Calculate the sum of beauty over all subsequences of the array of length exactly $k$. As this number can be very large, output it modulo $998244353$.
A sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements.
Input
The first line contains integers $n, k$ ($2 \le k \le n \le 1000$).
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le 10^5$).
Output
Output one integer — the sum of beauty over all subsequences of the array of length exactly $k$. As this number can be very large, output it modulo $998244353$.
Samples
4 3
1 7 3 5
8
5 5
1 10 100 1000 10000
9
Note
In the first example, there are $4$ subsequences of length $3$ — $[1, 7, 3]$, $[1, 3, 5]$, $[7, 3, 5]$, $[1, 7, 5]$, each of which has beauty $2$, so answer is $8$.
In the second example, there is only one subsequence of length $5$ — the whole array, which has the beauty equal to $|10-1| = 9$.