A12705. Array Beauty

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.

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 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 $998244353$ .

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 $|10-1| = 9$ .