F. Array Beauty
time limit per test
5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $$$998244353$$$.

Examples
Input
4 3
1 7 3 5
Output
8
Input
5 5
1 10 100 1000 10000
Output
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 $$$|10-1| = 9$$$.