For a sequence S of positive integers and positive integers k and l, S is said to belong to level (k,l) when one of the following conditions is satisfied:

* The length of S is 1, and its only element is k.
* There exist sequences T_1,T_2,...,T_m (m \geq l) belonging to level (k-1,l) such that the concatenation of T_1,T_2,...,T_m in this order coincides with S.



Note that the second condition has no effect when k=1, that is, a sequence belongs to level (1,l) only if the first condition is satisfied.

Given are a sequence of positive integers A_1,A_2,...,A_N and a positive integer L. Find the number of subsequences A_i,A_{i+1},...,A_j (1 \leq i \leq j \leq N) that satisfy the following condition:

* There exists a positive integer K such that the sequence A_i,A_{i+1},...,A_j belongs to level (K,L).

Constraints

* 1 \leq N \leq 2 \times 10^5
* 2 \leq L \leq N
* 1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N L
A_1 A_2 ... A_N


Output

Print the number of subsequences A_i,A_{i+1},...,A_j (1 \leq i \leq j \leq N) that satisfy the condition.

Examples

Input

9 3
2 1 1 1 1 1 1 2 3


Output

22


Input

9 2
2 1 1 1 1 1 1 2 3


Output

41


Input

15 3
4 3 2 1 1 1 2 3 2 2 1 1 1 2 2


Output

31
/**
 *    author:  tourist
 *    created: 08.12.2019 08:24:29       
**/
#include <bits/stdc++.h>

using namespace std;

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, len;
  cin >> n >> len;
  vector<int> a(n);
  vector<int> L(n);
  vector<int> R(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    L[i] = 1;
    R[i] = 1;
  }
  long long ans = n;
  set<pair<int, int>> s;
  set<int> alive;
  for (int i = 0; i < n; i++) {
    s.emplace(a[i], i);
    alive.insert(i);
  }
  while (!s.empty()) {
    int id = s.begin()->second;
    s.erase(s.begin());
    vector<int> pos(1, id);
    while (true) {
      auto it = alive.lower_bound(pos.back() + 1);
      if (it == alive.end() || a[*it] != a[id]) {
        break;
      }
      s.erase(make_pair(a[*it], *it));
      pos.push_back(*it);
    }
    int sz = (int) pos.size();
    if (sz < len) {
      continue;
    }
    {
      long long sumL = 0;
      for (int i = len - 1; i < sz; i++) {
        sumL += L[pos[i - len + 1]];
        ans += sumL * R[pos[i]];
      }
    }
    for (int x : pos) {
      alive.erase(x);
    }
    int new_sz = sz / len;
    vector<int> newL(new_sz);
    vector<int> newR(new_sz);
    for (int i = 0; i < sz; i++) {
      if (i >= len - 1) {
        newR[(i - (len - 1)) / len] += R[pos[i]];
      }
      if (i <= sz - len) {
        newL[new_sz - 1 - ((sz - len) - i) / len] += L[pos[i]];
      }
    }
    for (int i = 0; i < new_sz; i++) {
      alive.insert(pos[i]);
      L[pos[i]] = newL[i];
      R[pos[i]] = newR[i];
      a[pos[i]] += 1;
      s.emplace(a[pos[i]], pos[i]);
    }
    if (len <= new_sz) {
      long long sumL = 0;
      for (int i = len - 1; i < new_sz; i++) {
        sumL += L[pos[i - len + 1]];
        ans -= sumL * R[pos[i]];
      }
    }
  }
  cout << ans << '\n';
  return 0;
}
