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;
const int INFint = 2e9;
const long long INF = 2e18;
const long long MOD = 1000000007ll;
class SegmentTree {
 public:
  int n;
  vector<pair<int, int> > t;
  void modify(int pos, pair<int, int> val) {
    pos += n;
    for (t[pos] = max(t[pos], val); pos > 1; pos >>= 1)
      t[pos >> 1] = max(t[pos], t[pos ^ 1]);
  }
  pair<int, int> query(int l, int r) {
    pair<int, int> res = {0, -1};
    for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
      if (l & 1) res = max(res, t[l++]);
      if (r & 1) res = max(res, t[--r]);
    }
    return res;
  }
  SegmentTree(int n) : n(n) { t.resize(n << 1, {0, -1}); }
};
int main() {
  ios_base::sync_with_stdio(0);
  int n, d;
  cin >> n >> d;
  vector<long long> h(n);
  map<long long, int> comp;
  for (auto &x : h) {
    cin >> x;
    comp[x] = 0;
    comp[x - d] = 0;
    comp[x + d] = 0;
  }
  int sz = 0;
  for (auto x : comp) {
    comp[x.first] = sz++;
  }
  vector<int> anc(n, -1);
  SegmentTree sg(sz);
  for (int i = 0; i < n; i++) {
    int x = comp[h[i]];
    int lx = comp[h[i] - d];
    int bx = comp[h[i] + d];
    auto bst = max(sg.query(0, lx + 1), sg.query(bx, sz));
    anc[i] = bst.second;
    sg.modify(x, {bst.first + 1, i});
  }
  auto res = sg.query(0, sz);
  vector<int> ans;
  int v = res.second;
  while (v != -1) {
    ans.push_back(v);
    v = anc[v];
  }
  cout << res.first << endl;
  reverse(ans.begin(), ans.end());
  for (auto x : ans) cout << x + 1 << ' ';
  fprintf(stderr, "\nTIME = %lf\n", 1.0 * clock() / CLOCKS_PER_SEC);
  ;
  return 0;
}
