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 dove[100000];
int maxvalue[100000];
set<pair<long long, int> > sinistra;
set<pair<long long, int> > destra;
map<long long, int> last_time;
void stampa(int da) {
  if (maxvalue[da] != 1) stampa(dove[da]);
  cout << (da + 1) << " ";
}
int main(void) {
  int n, d;
  cin >> n >> d;
  for (int i = 0; i < n; i++) {
    long long num;
    cin >> num;
    dove[i] = i;
    maxvalue[i] = 1;
    set<pair<long long, int> >::iterator it =
        sinistra.upper_bound(make_pair(num - d, INT_MAX));
    if (sinistra.size()) it--;
    if (it != sinistra.end() && it->first <= num - d) {
      int maxvalue2 = it->second;
      dove[i] = last_time[it->first];
      maxvalue[i] = maxvalue2 + 1;
    }
    it = destra.lower_bound(make_pair((num + d), INT_MIN));
    if (it != destra.end() && it->second + 1 > maxvalue[i]) {
      int maxvalue2 = it->second;
      dove[i] = last_time[it->first];
      maxvalue[i] = maxvalue2 + 1;
    }
    sinistra.insert(make_pair(num, maxvalue[i]));
    it = sinistra.find(make_pair(num, maxvalue[i]));
    set<pair<long long, int> >::iterator succ = it;
    while (1) {
      succ++;
      if (succ == sinistra.end()) break;
      if (succ->second <= it->second) {
        set<pair<long long, int> >::iterator back = succ;
        back--;
        sinistra.erase(succ);
        succ = back;
      } else
        break;
    }
    set<pair<long long, int> >::iterator prec = it;
    prec--;
    if (prec != it && prec->second >= it->second) sinistra.erase(it);
    destra.insert(make_pair(num, maxvalue[i]));
    it = destra.find(make_pair(num, maxvalue[i]));
    prec = it;
    while (1) {
      if (prec == destra.begin()) break;
      prec--;
      if (prec->second <= it->second) {
        set<pair<long long, int> >::iterator back = prec;
        back++;
        destra.erase(prec);
        prec = back;
      }
    }
    succ = it;
    succ++;
    if (succ != destra.end() && succ->second >= it->second) destra.erase(it);
    last_time[num] = i;
  }
  int maxi = 0, dd = 0;
  for (int i = 0; i < n; i++)
    if (maxvalue[i] > maxi) {
      maxi = maxvalue[i];
      dd = i;
    }
  cout << maxvalue[dd] << endl;
  stampa(dd);
}
