1189_F. Array Beauty
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.
```python
from collections import defaultdict
import sys
input = sys.stdin.readline
'''
for CASES in range(int(input())):
n, m = map(int, input().split())
n = int(input())
A = list(map(int, input().split()))
S = input().strip()
sys.stdout.write(" ".join(map(str,ans))+"\n")
'''
inf = 100000000000000000  # 1e17
mod = 998244353

n, m = map(int, input().split())
A = [0] + sorted(list(map(int, input().split())))

ans = 0

f = [[0] * (n + 10) for _ in range(m + 10)]

for x in range(1,(A[n] - A[1]) // (m - 1) + 1):
    for i in range(1, n + 1):
        f[1][i] = 1
    for i in range(2, m + 1):
        sum = 0
        pre = 1
        for j in range(1, n + 1):
            while pre <= n and A[pre] + x <= A[j]:
                sum += f[i - 1][pre]
                sum %= mod
                pre += 1
            f[i][j] = sum
    for i in range(1, n + 1):
        ans += f[m][i]
        ans %= mod
print(ans)


# the end

```