Marmot found a row with n pillars. The i-th pillar has the height of hi meters. Starting from one pillar i1, Marmot wants to jump on the pillars i2, ..., ik. (1 ≤ i1 < i2 < ... < ik ≤ n). From a pillar i Marmot can jump on a pillar j only if i < j and |hi - hj| ≥ d, where |x| is the absolute value of the number x.

Now Marmot is asking you find out a jump sequence with maximal length and print it.

Input

The first line contains two integers n and d (1 ≤ n ≤ 105, 0 ≤ d ≤ 109).

The second line contains n numbers h1, h2, ..., hn (1 ≤ hi ≤ 1015).

Output

The first line should contain one integer k, the maximal length of a jump sequence.

The second line should contain k integers i1, i2, ..., ik (1 ≤ i1 < i2 < ... < ik ≤ n), representing the pillars' indices from the maximal length jump sequence.

If there is more than one maximal length jump sequence, print any.

Examples

Input

5 2
1 3 6 7 4


Output

4
1 2 3 5 


Input

10 3
2 1 3 6 9 11 7 3 20 18


Output

6
1 4 6 7 8 9 

Note

In the first example Marmot chooses the pillars 1, 2, 3, 5 with the heights 1, 3, 6, 4. Another jump sequence of length 4 is 1, 2, 4, 5.
#include <bits/stdc++.h>
using namespace std;
int DP[100005];
int choice[100005];
long long arr[100005];
int main() {
  ios_base::sync_with_stdio(0);
  int n, d;
  cin >> n >> d;
  for (int i = 0; i < n; i++) cin >> arr[i];
  set<pair<long long, int> > hig, les;
  for (int i = n - 1; i >= 0; i--) {
    set<pair<long long, int> >::iterator it1, it2;
    int res = 1, tmp = -1;
    it1 = hig.lower_bound(make_pair(arr[i], 0));
    it2 = les.lower_bound(make_pair(arr[i], 0));
    if (it2 != les.end()) {
      pair<long long, int> temp = *it2;
      if (res < DP[temp.second] + 1)
        res = DP[temp.second] + 1, tmp = temp.second;
    }
    if (hig.size() != 0) {
      pair<long long, int> temp = *it1;
      bool test = 0;
      if (it1 == hig.end())
        it1--;
      else if (temp.first != arr[i]) {
        if (it1 == hig.begin())
          test = 1;
        else
          it1--;
      }
      if (!test) {
        temp = *it1;
        if (res < DP[temp.second] + 1)
          res = DP[temp.second] + 1, tmp = temp.second;
      }
    }
    DP[i] = res;
    choice[i] = tmp;
    it1 = hig.lower_bound(make_pair(arr[i] + d, 0));
    it2 = les.lower_bound(make_pair(arr[i] - d, 0));
    bool add = 0;
    if (hig.size() == 0 || it1 == hig.begin())
      add = 1;
    else {
      set<pair<long long, int> >::iterator ittemp = it1;
      ittemp--;
      pair<long long, int> temp = *ittemp;
      if (DP[i] > DP[temp.second]) add = 1;
    }
    if (add) {
      while (it1 != hig.end()) {
        pair<long long, int> temp = *it1;
        if (DP[i] < DP[temp.second]) break;
        set<pair<long long, int> >::iterator ittemp = it1;
        ittemp++;
        hig.erase(it1);
        it1 = ittemp;
      }
      hig.insert(make_pair(arr[i] + d, i));
      add = 0;
    }
    if (it2 == les.end())
      add = 1;
    else {
      pair<long long, int> temp = *it2;
      if (DP[i] > DP[temp.second]) add = 1;
    }
    if (add) {
      bool test = 0;
      if (les.size() != 0) {
        pair<long long, int> temp = *it2;
        if (temp.first != arr[i] - d) {
          if (it2 == les.begin())
            test = 1;
          else
            it2--;
        }
      }
      while (les.size() != 0 && !test) {
        pair<long long, int> temp = *it2;
        if (DP[i] < DP[temp.second]) break;
        set<pair<long long, int> >::iterator ittemp = it2;
        if (it2 == les.begin()) {
          les.erase(it2);
          break;
        }
        ittemp--;
        les.erase(it2);
        it2 = ittemp;
      }
      les.insert(make_pair(arr[i] - d, i));
    }
  }
  int ch = 0;
  for (int i = 1; i < n; i++)
    if (DP[ch] < DP[i]) ch = i;
  cout << DP[ch] << "\n";
  while (ch != -1) {
    cout << ch + 1 << " ";
    ch = choice[ch];
  }
  return 0;
}
