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 N = 1e5 + 100, M = 3 * N, inF = N;
int n, dp[N], bk[N];
long long d, h[N];
pair<int, int> seg[M << 2];
vector<long long> vec;
pair<int, int> get(int l, int r, int v = 1, int s = 0, int e = M) {
  if (r <= s || e <= l) return pair<int, int>(-inF, -inF);
  if (l <= s && e <= r) return seg[v];
  int mid = (s + e) >> 1, lc = v << 1, rc = lc | 1;
  return max(get(l, r, lc, s, mid), get(l, r, rc, mid, e));
}
void change(int dex, pair<int, int> val, int v = 1, int s = 0, int e = M) {
  if (dex < s || e <= dex) return;
  seg[v] = max(seg[v], val);
  if (e - s == 1) return;
  int mid = (s + e) >> 1, lc = v << 1, rc = lc | 1;
  change(dex, val, lc, s, mid);
  change(dex, val, rc, mid, e);
}
int f(long long a) {
  return lower_bound(vec.begin(), vec.end(), a) - vec.begin();
}
int g(long long a) {
  return upper_bound(vec.begin(), vec.end(), a) - vec.begin();
}
int main() {
  ios::sync_with_stdio(false);
  fill(seg, seg + (M << 2), pair<int, int>(-inF, -inF));
  cin >> n >> d;
  for (int i = 0; i < n; i++) {
    cin >> h[i];
    vec.push_back(h[i] - d);
    vec.push_back(h[i]);
    vec.push_back(h[i] + d);
  }
  sort(vec.begin(), vec.end());
  vec.resize(unique(vec.begin(), vec.end()) - vec.begin());
  dp[0] = 1;
  change(f(h[0]), pair<int, int>(dp[0], 0));
  for (int i = 1; i < n; i++) {
    int a = g(h[i] - d), b = f(h[i] + d);
    pair<int, int> p = max(get(0, a), get(b, M));
    dp[i] = max(1, p.first + 1), bk[i] = p.second;
    change(f(h[i]), pair<int, int>(dp[i], i));
  }
  int dex = 0;
  for (int i = 0; i < n; i++)
    if (dp[i] > dp[dex]) dex = i;
  int maxi = dp[dex];
  vector<int> ans;
  for (int i = 0; i < maxi; i++) ans.push_back(dex), dex = bk[dex];
  reverse(ans.begin(), ans.end());
  cout << maxi << '\n';
  for (int dex : ans) cout << dex + 1 << ' ';
  return 0;
}
