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 $|10-1| = 9$.