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 MOD = 1000000007;
const int NMAX = 300010;
const double E = 1e-8;
const double PI = acos(-1);
int n, m, stest;
int d;
set<long long> St;
long long st[NMAX], h[NMAX];
pair<int, int> Tree[4 * NMAX];
int dp[NMAX], trace[NMAX];
pair<int, int> cmp(pair<int, int> a, pair<int, int> b) {
  if (a.first > b.first)
    return a;
  else
    return b;
}
void update(int i, int lo, int hi, int u, int x, int vt) {
  if (lo == hi) {
    Tree[i] = cmp(Tree[i], pair<int, int>(x, vt));
    return;
  }
  int mid = (lo + hi) >> 1;
  if (u <= mid)
    update(2 * i, lo, mid, u, x, vt);
  else
    update(2 * i + 1, mid + 1, hi, u, x, vt);
  Tree[i] = cmp(Tree[2 * i], Tree[2 * i + 1]);
}
pair<int, int> query(int i, int lo, int hi, int u, int v) {
  if (v < lo || hi < u) return pair<int, int>(0, 0);
  if (u <= lo && hi <= v) return Tree[i];
  int mid = (lo + hi) >> 1;
  return cmp(query(2 * i, lo, mid, u, v), query(2 * i + 1, mid + 1, hi, u, v));
}
void truy(int x) {
  if (x == 0) return;
  truy(trace[x]);
  cout << x << " ";
}
int main() {
  ios::sync_with_stdio(false);
  cin >> n >> d;
  for (int i = 1; i <= n; i++) {
    cin >> h[i];
    St.insert(h[i]);
    St.insert(h[i] - d);
    St.insert(h[i] + d);
  }
  for (set<long long>::iterator it = St.begin(); it != St.end(); it++)
    st[++m] = *it;
  int ans = 0, vt = 0;
  for (int i = 1; i <= n; i++) {
    int pos = lower_bound(st + 1, st + m + 1, h[i]) - st;
    int u = lower_bound(st + 1, st + m + 1, h[i] - d) - st;
    int v = lower_bound(st + 1, st + m + 1, h[i] + d) - st;
    pair<int, int> res = cmp(query(1, 1, m, 1, u), query(1, 1, m, v, m));
    dp[i] = res.first + 1;
    trace[i] = res.second;
    update(1, 1, m, pos, dp[i], i);
    if (dp[i] > ans) {
      ans = dp[i];
      vt = i;
    }
  }
  cout << ans << endl;
  truy(vt);
  return 0;
}
