#include <bits/stdc++.h>
static const int MAXN = 1e3 + 5;
static const int mod = 998244353;
using namespace std;
static int f[MAXN][MAXN], s[MAXN][MAXN];
static int a[MAXN], n, k, ans;
int main() {
  scanf("%d %d", &n, &k);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
  sort(a + 1, a + n + 1);
  for (int x = 1; x <= (a[n] - a[1]) / (k - 1); ++x) {
    for (int i = 0; i <= n; ++i)
      for (int j = 0; j <= k; ++j) f[i][j] = s[i][j] = 0;
    for (int i = 1; i <= n; ++i) f[i][1] = 1, s[i][1] = i;
    for (int j = 2; j <= k; ++j) {
      int tot = 0;
      for (int i = 1; i <= n; ++i) {
        while (tot < i && a[i] - a[tot] >= x) tot++;
        if (tot && a[i] - a[tot] < x) tot--;
        f[i][j] = s[tot][j - 1];
        s[i][j] = (s[i - 1][j] + f[i][j]) % mod;
      }
    }
    ans = (ans + s[n][k]) % mod;
  }
  printf("%d", ans);
  return 0;
}

### Prompt

Your task is to create a CPP solution to the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
static const int MAXN = 1e3 + 5;
static const int mod = 998244353;
using namespace std;
static int f[MAXN][MAXN], s[MAXN][MAXN];
static int a[MAXN], n, k, ans;
int main() {
  scanf("%d %d", &n, &k);
  for (int i = 1; i <= n; ++i) scanf("%d", &a[i]);
  sort(a + 1, a + n + 1);
  for (int x = 1; x <= (a[n] - a[1]) / (k - 1); ++x) {
    for (int i = 0; i <= n; ++i)
      for (int j = 0; j <= k; ++j) f[i][j] = s[i][j] = 0;
    for (int i = 1; i <= n; ++i) f[i][1] = 1, s[i][1] = i;
    for (int j = 2; j <= k; ++j) {
      int tot = 0;
      for (int i = 1; i <= n; ++i) {
        while (tot < i && a[i] - a[tot] >= x) tot++;
        if (tot && a[i] - a[tot] < x) tot--;
        f[i][j] = s[tot][j - 1];
        s[i][j] = (s[i - 1][j] + f[i][j]) % mod;
      }
    }
    ans = (ans + s[n][k]) % mod;
  }
  printf("%d", ans);
  return 0;
}

```