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;
vector<long long int> v2;
vector<pair<long long int, int> > v1;
long long int a[100005] = {0};
int pos[100005] = {0}, ans[100005][2] = {0}, segtree[400005] = {0};
int query(int qlow, int qhigh, int low, int high, int pos) {
  if (qlow <= low && qhigh >= high) return segtree[pos];
  if (qlow > high || qhigh < low) {
    return 100003;
  }
  int mid = (low + high) / 2;
  int n3 = query(qlow, qhigh, low, mid, 2 * pos + 1);
  int n4 = query(qlow, qhigh, mid + 1, high, 2 * pos + 2);
  if (ans[n3][0] >= ans[n4][0])
    return n3;
  else
    return n4;
}
void update(int val, int index, int n) {
  int i = 0, low = 0, high = n - 1;
  while (true) {
    if (low == high) break;
    int mid = (high + low) / 2;
    if (index <= mid) {
      high = mid;
      i = i * 2 + 1;
    } else {
      low = mid + 1;
      i = i * 2 + 2;
    }
  }
  segtree[i] = val;
  index = i;
  index = (index - 1) / 2;
  while (index != 0) {
    int n1 = segtree[2 * index + 1];
    int n2 = segtree[2 * index + 2];
    if (ans[n1][0] >= ans[n2][0])
      segtree[index] = n1;
    else
      segtree[index] = n2;
    index = (index - 1) / 2;
  }
  int n1 = segtree[2 * index + 1];
  int n2 = segtree[2 * index + 2];
  if (ans[n1][0] >= ans[n2][0])
    segtree[index] = n1;
  else
    segtree[index] = n2;
}
int main() {
  for (int i = 0; i < 400000; i++) segtree[i] = 100003;
  long long int n, d;
  cin >> n >> d;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    v1.push_back({a[i], i});
  }
  sort(v1.begin(), v1.end());
  for (int i = 0; i < n; i++) {
    pos[v1[i].second] = i;
    v2.push_back(v1[i].first);
  }
  for (int i = 0; i < n; i++) {
    int idx1 = lower_bound(v2.begin(), v2.end(), a[i] + d) - v2.begin();
    int idx2 = upper_bound(v2.begin(), v2.end(), a[i] - d) - v2.begin();
    idx2--;
    int i1, i2;
    if (idx2 >= 0) {
      i1 = (query(0, idx2, 0, n - 1, 0));
      if (ans[i1][0] + 1 > ans[i][0]) {
        ans[i][0] = ans[i1][0] + 1;
        ans[i][1] = i1;
      }
    }
    if (idx1 <= n - 1) {
      i2 = (query(idx1, n - 1, 0, n - 1, 0));
      if (ans[i2][0] + 1 > ans[i][0]) {
        ans[i][0] = ans[i2][0] + 1;
        ans[i][1] = i2;
      }
    }
    update(i, pos[i], n);
  }
  int max1 = 0, pos = 0;
  for (int i = 0; i < n; i++) {
    if (ans[i][0] > max1) {
      max1 = ans[i][0];
      pos = i;
    }
  }
  cout << max1 << "\n";
  int fin[100005] = {0}, len = 0;
  while (ans[pos][0] != 1 && ans[pos][0] <= 100000) {
    fin[len++] = pos + 1;
    pos = ans[pos][1];
  }
  fin[len++] = pos + 1;
  for (int i = len - 1; i >= 0; i--) cout << fin[i] << " ";
}
