Let's call beauty of an array b_1, b_2, …, b_n (n > 1) — min_{1 ≤ i < j ≤ n} |b_i - b_j|.

You're given an array a_1, a_2, … 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 ≤ k ≤ n ≤ 1000).

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 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.
import java.util.Arrays;
import java.util.Scanner;

public class Beauty {
	
	
	public static void main(String[] args) {
	
	int m = 998244353;
	int b[] = new int[1012];
	int dp[][] = new int[1012][1012];
	int l;
	
	Scanner scan = new Scanner(System.in);
	int n = scan.nextInt();
	int k = scan.nextInt();
	
	for(int i = 1; i<=n; i++) {
		b[i] = scan.nextInt();
	}
	scan.close();
	
	Arrays.sort(b,1,n + 1);
	
	int ans = 0;
	for(int p = 1; p <= b[n]/(k-1); p++) {
		dp[0][0] = 1;
		l = 1;
		for(int i = 1; i <= n; i++) {
			while(b[i] >= b[l] + p) {
				l++;
			}
			dp[i][0] = dp[i-1][0];
			for(int j = 1; j <= k; j++) {
				dp[i][j] = (dp[i-1][j] + dp[l-1][j-1]) % m;
			}
		}
		ans = (ans + dp[n][k]) % m;
	}
	
	System.out.println(ans);  	
}
}
