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 N, D;
long long H;
pair<int, int> las[100000];
set<pair<long long, pair<int, int> > > bf, af;
int main() {
  scanf("%d%d", &N, &D);
  for (int(i) = 0; (i) < (N); (i)++) {
    cin >> H;
    las[i] = make_pair(1, -1);
    set<pair<long long, pair<int, int> > >::iterator it =
        af.lower_bound(make_pair(H, make_pair((1 << 29), (1 << 29))));
    if (it != af.begin())
      it--, las[i] =
                max(las[i], make_pair(it->second.first + 1, it->second.second));
    it = bf.upper_bound(make_pair(H, make_pair(-1, -1)));
    if (it != bf.end()) {
      las[i] = max(las[i], make_pair(it->second.first + 1, it->second.second));
    }
    pair<int, int> tmp = make_pair(las[i].first, i);
    while (1) {
      it = af.lower_bound(make_pair(H + D, make_pair(-1, -1)));
      if (it != af.begin()) {
        it--;
        if (it->second > tmp) goto lb1;
        it++;
      }
      if (it == af.end()) break;
      if (it->second < tmp)
        af.erase(it);
      else
        break;
    }
    af.insert(make_pair(H + D, tmp));
  lb1:;
    while (1) {
      it = bf.lower_bound(make_pair(H - D, make_pair((1 << 29), (1 << 29))));
      if (it != bf.end() && it->second > tmp) goto lb2;
      if (it == bf.begin()) break;
      it--;
      if (it->second < tmp)
        bf.erase(it);
      else
        break;
    }
    bf.insert(make_pair(H - D, tmp));
  lb2:;
  }
  pair<int, int> at = make_pair(-(1 << 29), -(1 << 29));
  for (int(i) = 0; (i) < (N); (i)++) at = max(at, make_pair(las[i].first, i));
  vector<int> ans;
  int pp = at.second;
  while (pp != -1) {
    ans.push_back(pp);
    pp = las[pp].second;
  }
  printf("%d\n", ans.size());
  for (int i = ans.size() - 1; i >= 0; i--)
    printf("%d%c", ans[i] + 1, i == 0 ? '\n' : ' ');
}
