C. Array Beauty
dp
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 \(|10-1| = 9\).