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.
#include <bits/stdc++.h>
const int p = 998244353;
int add32(int x, int y) {
  int res = x + y;
  if (res >= p) res -= p;
  return res;
}
int sub32(int x, int y) {
  int res = x - y;
  if (res < 0) res += p;
  return res;
}
int mul32(int x, int y) { return int64_t(x) * y % p; }
struct Solution {
  int n, k;
  std::vector<int> as;
  std::vector<std::vector<int>> dyn;
  std::vector<int> combs;
  void run(std::istream &in, std::ostream &out) {
    in >> n >> k;
    as.assign(n, 0);
    for (int i = 0; i < n; i++) {
      in >> as[i];
    }
    std::sort(as.begin(), as.end());
    dyn.assign(n, std::vector<int>(k));
    combs.resize(100000 / (k - 1) + 2);
    std::cerr << combs.size() << std::endl;
    for (int i = 0; i < combs.size(); i++) {
      std::fill(dyn[0].begin(), dyn[0].end(), 0);
      dyn[0][0] = 1;
      int prev = -1;
      for (int j = 1; j < n; j++) {
        while (prev + 1 < j && as[prev + 1] <= as[j] - i) prev++;
        if (prev < 0) {
          dyn[j] = dyn[j - 1];
          dyn[j][0] = add32(1, dyn[j][0]);
        } else {
          dyn[j][0] = add32(1, dyn[j - 1][0]);
          for (int l = 1; l < k; l++) {
            dyn[j][l] = add32(dyn[j - 1][l], dyn[prev][l - 1]);
          }
        }
      }
      combs[i] = dyn[n - 1][k - 1];
    }
    int ans = 0;
    for (int i = 0; i + 1 < combs.size(); i++) {
      int diff = sub32(combs[i], combs[i + 1]);
      ans = add32(ans, mul32(diff, i));
    }
    out << ans << "\n";
  }
};
int main() {
  std::cin.sync_with_stdio(false);
  std::cin.tie(nullptr);
  Solution().run(std::cin, std::cout);
  return 0;
}
