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 maxt = 300001;
typedef int mang[maxt + 10];
struct mystr {
  int val[4];
};
mang bit1, bit2;
mystr a[100010];
int n, dem, vt = 1;
long long d, m;
vector<pair<long long, pair<int, int>>> b;
int kq[100010];
vector<int> s;
int getbit(int x, mang bit) {
  int res = -maxt;
  for (; x > 0; x -= x & (-x)) res = max(res, bit[x]);
  return res;
}
void updatebit(int x, int val, mang& bit) {
  for (; x <= maxt; x += x & (-x)) bit[x] = max(bit[x], val);
}
int main() {
  ios::sync_with_stdio(0);
  cin >> n >> d;
  for (int i = 1; i <= n; i++) {
    cin >> m;
    b.push_back({m, {i, 1}});
    b.push_back({m - d, {i, 2}});
    b.push_back({m + d, {i, 3}});
  }
  b.push_back({(int)-1e18, {0, 0}});
  sort(b.begin(), b.end());
  for (int i = 1; i < b.size(); i++) {
    if (b[i].first != b[i - 1].first) dem++;
    a[b[i].second.first].val[b[i].second.second] = dem;
  }
  for (int i = 1; i <= n; i++) {
    int longt =
        max(getbit(a[i].val[2], bit1), getbit(maxt - a[i].val[3], bit2)) + 1;
    updatebit(a[i].val[1], longt, bit1);
    updatebit(maxt - a[i].val[1], longt, bit2);
    kq[i] = longt;
    if (kq[i] >= kq[vt]) vt = i;
  }
  cout << kq[vt] << "\n";
  for (int i = vt; i >= 1; i--)
    if (kq[vt] == kq[i] + 1 &&
        (a[i].val[1] <= a[vt].val[2] || a[i].val[1] >= a[vt].val[3])) {
      s.push_back(vt);
      vt = i;
    }
  cout << vt << " ";
  for (int i = s.size() - 1; i >= 0; i--) cout << s[i] << " ";
  return 0;
}
