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C. Array Beauty

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet'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 $$$|10-1| = 9$$$.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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