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 double EPS = 1e-7;
const long long INF = (long long)(2e18 + 0.5);
const int MAXN = 100500;
class SegmentTree {
 public:
  SegmentTree *left, *right;
  pair<int, int> value;
  SegmentTree() : left(0), right(0), value(-1, -1) {}
};
pair<int, int> get(SegmentTree* v, long long l, long long r, long long tl,
                   long long tr) {
  if (!v || tl > tr)
    return make_pair(-1, -1);
  else if (tl == l && r == tr)
    return v->value;
  assert(l <= tl && tr <= r && l <= r && tl <= tr);
  long long m = (l + r) >> 1LL;
  pair<int, int> result = make_pair(-1, -1);
  if (tl <= m) result = get(v->left, l, m, tl, min(tr, m));
  if (tr > m) result = max(result, get(v->right, m + 1, r, max(tl, m + 1), tr));
  return result;
}
void insert(SegmentTree* v, long long l, long long r, long long key,
            pair<int, int> value) {
  assert(v && l <= r);
  if (l == r)
    v->value = max(v->value, value);
  else {
    long long m = (l + r) >> 1LL;
    if (key <= m) {
      if (!v->left) v->left = new SegmentTree();
      insert(v->left, l, m, key, value);
    } else {
      if (!v->right) v->right = new SegmentTree();
      insert(v->right, m + 1, r, key, value);
    }
    v->value = max(v->value, value);
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int n;
  cin >> n;
  long long d;
  cin >> d;
  vector<long long> hs(n);
  for (int i = 0; i < n; cin >> hs[i], ++i)
    ;
  SegmentTree* root = new SegmentTree();
  vector<int> dp(n), p(n);
  int last = -1;
  for (int i = 0; i < n; ++i) {
    dp[i] = 1;
    p[i] = -1;
    pair<int, int> best =
        max(get(root, 1, INF, 1, hs[i] - d), get(root, 1, INF, hs[i] + d, INF));
    if (best.first > -1) {
      dp[i] = best.first + 1;
      p[i] = best.second;
    }
    insert(root, 1, INF, hs[i], make_pair(dp[i], i));
    if (last == -1 || dp[i] > dp[last]) last = i;
  }
  int ans = dp[last];
  cout << ans << "\n";
  vector<int> path;
  for (int v = last; v != -1; v = p[v]) path.push_back(v);
  for (int i = (int)path.size() - 1; i >= 0; cout << path[i] + 1 << " ", --i)
    ;
  cout << "\n";
  return 0;
}
