#include <bits/stdc++.h>
using namespace std;
const int maxn = 1007;
const int inf = INT_MAX;
const long long inff = 1e18;
const long long mod = 998244353;
long long n, k;
long long a[maxn], maxx = -1;
long long dp[maxn][maxn];
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  for (long long i = 1; i <= n; i++) cin >> a[i], maxx = max(maxx, a[i]);
  sort(a + 1, a + n + 1);
  long long C = min(maxx, maxx / (k - 1) + 2);
  for (long long i = 0; i <= n; i++) dp[i][0] = 1;
  long long ans = 0, lastans = 0;
  for (long long _ = C; _ >= 1; _--) {
    long long last = 0;
    for (long long i = 1; i <= n; i++) {
      while (a[i] - a[last + 1] >= _) last++;
      for (long long j = 1; j <= k; j++) {
        dp[i][j] = (dp[i - 1][j] + dp[last][j - 1]) % mod;
      }
    }
    ans = (ans + (dp[n][k] + mod - lastans) * _ % mod) % mod;
    lastans = dp[n][k];
  }
  cout << ans << endl;
}

### Prompt

Generate 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>
using namespace std;
const int maxn = 1007;
const int inf = INT_MAX;
const long long inff = 1e18;
const long long mod = 998244353;
long long n, k;
long long a[maxn], maxx = -1;
long long dp[maxn][maxn];
int32_t main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  for (long long i = 1; i <= n; i++) cin >> a[i], maxx = max(maxx, a[i]);
  sort(a + 1, a + n + 1);
  long long C = min(maxx, maxx / (k - 1) + 2);
  for (long long i = 0; i <= n; i++) dp[i][0] = 1;
  long long ans = 0, lastans = 0;
  for (long long _ = C; _ >= 1; _--) {
    long long last = 0;
    for (long long i = 1; i <= n; i++) {
      while (a[i] - a[last + 1] >= _) last++;
      for (long long j = 1; j <= k; j++) {
        dp[i][j] = (dp[i - 1][j] + dp[last][j - 1]) % mod;
      }
    }
    ans = (ans + (dp[n][k] + mod - lastans) * _ % mod) % mod;
    lastans = dp[n][k];
  }
  cout << ans << endl;
}

```