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 = 100005;
long long h[MAXN], th[MAXN];
int nxt[MAXN];
struct data {
  int len, loc;
  data() {}
  data(int _len, int _loc) : len(_len), loc(_loc) {}
  data operator+(const data &t) const { return len >= t.len ? *this : t; }
};
struct node {
  int l, r, m;
  data v;
} s[MAXN << 2];
void push_up(int n) { s[n].v = s[n << 1].v + s[n << 1 | 1].v; }
void build(int l, int r, int n) {
  int m = (l + r) >> 1;
  s[n].l = l;
  s[n].r = r;
  s[n].m = m;
  if (r - l == 1) {
    s[n].v = data(0, 0);
    return;
  }
  build(l, m, n << 1);
  build(m, r, n << 1 | 1);
  push_up(n);
}
void update(int p, data v, int n) {
  if (s[n].l == p && s[n].r == p + 1) {
    s[n].v = s[n].v + v;
    return;
  }
  if (p < s[n].m)
    update(p, v, n << 1);
  else
    update(p, v, n << 1 | 1);
  push_up(n);
}
data query(int l, int r, int n) {
  if (r <= l) return data(0, 0);
  if (s[n].l == l && s[n].r == r) return s[n].v;
  if (r <= s[n].m) return query(l, r, n << 1);
  if (l >= s[n].m) return query(l, r, n << 1 | 1);
  return query(l, s[n].m, n << 1) + query(s[n].m, r, n << 1 | 1);
}
int main() {
  int n;
  long long d;
  scanf("%d%I64d", &n, &d);
  for (int i = 1; i <= n; i++) scanf("%I64d", &h[i]);
  memcpy(th, h + 1, n * sizeof(long long));
  sort(th, th + n);
  int tot = unique(th, th + n) - th;
  build(1, tot + 1, 1);
  int res = 0, st = 0;
  for (int i = n; i >= 1; i--) {
    int l = upper_bound(th, th + tot, h[i] - d) - th;
    int r = lower_bound(th, th + tot, h[i] + d) - th + 1;
    data t = query(1, l + 1, 1) + query(r, tot + 1, 1);
    nxt[i] = t.loc;
    if (res < t.len + 1) {
      res = t.len + 1;
      st = i;
    }
    int p = lower_bound(th, th + tot, h[i]) - th + 1;
    update(p, data(t.len + 1, i), 1);
  }
  printf("%d\n", res);
  for (int i = st; i; i = nxt[i]) printf("%d ", i);
  return 0;
}
