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;
int xx[4] = {0, 0, 1, -1};
int yy[4] = {1, -1, 0, 0};
int n, d;
struct re {
  long long x;
  int i;
};
long long a[int(1e5 + 100)];
int f[int(1e5 + 100)];
re c[int(1e5 + 100)];
int t[4 * int(1e5 + 100)];
int r, q[int(1e5 + 100)], p[int(1e5 + 100)];
void update(long long a, long long b, int l, int r, int node, int gt) {
  if (c[l].x > b || c[r].x < a) return;
  if (a <= c[l].x && c[r].x <= b) {
    t[node] = max(t[node], gt);
    return;
  }
  update(a, b, l, (l + r) / 2, node * 2, gt);
  update(a, b, (l + r) / 2 + 1, r, node * 2 + 1, gt);
}
int w[int(1e5 + 100)];
void build(int l, int r, int node) {
  if (l == r) {
    w[l] = node;
    return;
  }
  build(l, (l + r) / 2, node * 2);
  build((l + r) / 2 + 1, r, node * 2 + 1);
}
int get(int x) {
  int node = w[x], res = 0;
  while (node != 0) {
    res = max(res, t[node]);
    node /= 2;
  }
  return res;
}
bool cmp(re a, re b) { return a.x < b.x; }
long long aabs(long long x) {
  if (x < 0) return -x;
  return x;
}
int main() {
  scanf("%d%d", &n, &d);
  for (int i = (1), _b = (n); i <= _b; i++) {
    scanf("%I64d", &a[i]);
    c[i].x = a[i];
    c[i].i = i;
  }
  sort(c + 1, c + 1 + n, cmp);
  for (int i = (1), _b = (n); i <= _b; i++) p[c[i].i] = i;
  build(1, n, 1);
  int x = 0;
  for (int i = (1), _b = (n); i <= _b; i++) {
    f[i] = get(p[i]) + 1;
    if (c[1].x <= a[i] - d) update(c[1].x, a[i] - d, 1, n, 1, f[i]);
    if (a[i] + d <= c[n].x) update(a[i] + d, c[n].x, 1, n, 1, f[i]);
    if (f[i] > f[x]) {
      x = i;
    }
  }
  cout << f[x] << endl;
  r++;
  q[r] = x;
  while (f[x] != 1) {
    for (int i = (x - 1), _a = (0); i >= _a; i--)
      if (f[i] == f[x] - 1 && aabs(a[i] - a[x]) >= d) {
        r++;
        q[r] = i;
        x = i;
        break;
      }
  }
  for (int i = (r), _a = (1); i >= _a; i--) printf("%d ", q[i]);
}
