#include <bits/stdc++.h>
const int N = 1005;
const int MOD = 998244353;
int n, k, a[N], f[N][N], cnt[100005];
int solve(int x) {
  for (int i = 0; i <= n; i++)
    for (int j = 0; j <= k; j++) f[i][j] = 0;
  f[0][0] = 1;
  int p = 0;
  for (int i = 1; i <= n; i++) {
    while (p < i && a[i] - a[p + 1] >= x) p++;
    f[i][0] = 1;
    for (int j = 1; j <= std::min(i, k); j++)
      f[i][j] = (f[p][j - 1] + f[i - 1][j]) % MOD;
  }
  return f[n][k];
}
int main() {
  scanf("%d%d", &n, &k);
  int mx = 0;
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]), mx = std::max(mx, a[i]);
  std::sort(a + 1, a + n + 1);
  int T = mx / (k - 1);
  for (int i = 1; i <= T; i++) cnt[i] = solve(i);
  int ans = 0;
  for (int i = 1; i <= T; i++)
    (ans += (long long)i * (cnt[i] - cnt[i + 1]) % MOD) %= MOD;
  ans += ans < 0 ? MOD : 0;
  printf("%d\n", ans);
  return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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>
const int N = 1005;
const int MOD = 998244353;
int n, k, a[N], f[N][N], cnt[100005];
int solve(int x) {
  for (int i = 0; i <= n; i++)
    for (int j = 0; j <= k; j++) f[i][j] = 0;
  f[0][0] = 1;
  int p = 0;
  for (int i = 1; i <= n; i++) {
    while (p < i && a[i] - a[p + 1] >= x) p++;
    f[i][0] = 1;
    for (int j = 1; j <= std::min(i, k); j++)
      f[i][j] = (f[p][j - 1] + f[i - 1][j]) % MOD;
  }
  return f[n][k];
}
int main() {
  scanf("%d%d", &n, &k);
  int mx = 0;
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]), mx = std::max(mx, a[i]);
  std::sort(a + 1, a + n + 1);
  int T = mx / (k - 1);
  for (int i = 1; i <= T; i++) cnt[i] = solve(i);
  int ans = 0;
  for (int i = 1; i <= T; i++)
    (ans += (long long)i * (cnt[i] - cnt[i + 1]) % MOD) %= MOD;
  ans += ans < 0 ? MOD : 0;
  printf("%d\n", ans);
  return 0;
}

```