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 maxN = 1e5 + 5;
set<long long> s;
long long h[maxN], d;
vector<long long> second;
pair<int, int> it[maxN * 3 * 8];
long long n;
int dp[maxN], tr[maxN];
int cnt, res[maxN];
pair<int, int> getMax(pair<int, int> a, pair<int, int> b) {
  return (a.first > b.first ? a : b);
}
void Init(int i, int l, int r) {
  if (l == r) {
    it[i] = pair<int, int>(0, 0);
    return;
  }
  int mid = (l + r) / 2;
  Init(i * 2, l, mid);
  Init(i * 2 + 1, mid + 1, r);
  it[i] = getMax(it[i * 2], it[i * 2 + 1]);
}
void Update(int i, int l, int r, int x, int y, int pos) {
  if (l > x || r < x) return;
  if (l == r) {
    it[i] = getMax(it[i], pair<int, int>(y, pos));
    return;
  }
  int mid = (l + r) / 2;
  Update(i * 2, l, mid, x, y, pos);
  Update(i * 2 + 1, mid + 1, r, x, y, pos);
  it[i] = getMax(it[i * 2], it[i * 2 + 1]);
}
pair<int, int> Get(int i, int l, int r, int u, int v) {
  if (l > v || r < u) return pair<int, int>(0, 0);
  if (l >= u && r <= v) return it[i];
  int mid = (l + r) / 2;
  return getMax(Get(i * 2, l, mid, u, v), Get(i * 2 + 1, mid + 1, r, u, v));
}
void Trace(int u) {
  if (u == 0) return;
  Trace(tr[u]);
  ++cnt;
  res[cnt] = u;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n >> d;
  for (int i = 1; i <= n; ++i) {
    cin >> h[i];
    s.insert(h[i]);
    s.insert(h[i] - d);
    s.insert(h[i] + d);
  }
  second.push_back(-(long long)1e16);
  for (set<long long>::iterator it = s.begin(); it != s.end(); ++it)
    second.push_back(*it);
  int m = (int)second.size() - 1;
  Init(1, 1, n);
  for (int i = 1; i <= n; ++i) {
    int p1 = (lower_bound(second.begin(), second.end(), h[i]) - second.begin());
    int p2 =
        (lower_bound(second.begin(), second.end(), h[i] - d) - second.begin());
    int p3 =
        (lower_bound(second.begin(), second.end(), h[i] + d) - second.begin());
    pair<int, int> value = max(Get(1, 1, m, 1, p2), Get(1, 1, m, p3, m));
    dp[i] = dp[value.second] + 1;
    tr[i] = value.second;
    Update(1, 1, m, p1, dp[i], i);
  }
  int pos = 0, maxd = 0;
  for (int i = 1; i <= n; ++i)
    if (maxd < dp[i]) {
      maxd = dp[i];
      pos = i;
    }
  Trace(pos);
  printf("%d\n", cnt);
  for (int i = 1; i <= cnt; ++i) printf("%d ", res[i]);
  return 0;
}
