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>
#pragma comment(linker, "/STACK:256000000")
using namespace std;
struct item {
  long long count, height;
  item *l, *r;
  item(long long count, long long height, item *l, item *r)
      : count(count), height(height), l(l), r(r) {}
};
typedef item *pitem;
int n;
long long d;
long long a[100007];
long long dp[100007];
item *root;
void unite(pitem t, pitem l, pitem r) {
  long long count = 0;
  if (l) count = max(count, l->count);
  if (r) count = max(count, r->count);
  long long height = 0;
  if (l && count == l->count) height = l->height;
  if (r && count == r->count) height = r->height;
  t->count = count;
  t->height = height;
}
void upd(pitem &t, long long l, long long r, long long x, long long val) {
  if (!t) t = new item(0, 0, NULL, NULL);
  if (l == r) {
    t->height = x;
    t->count = max(t->count, val);
    return;
  }
  long long lr = (l + r) >> 1;
  if (x <= lr)
    upd(t->l, l, lr, x, val);
  else
    upd(t->r, lr + 1, r, x, val);
  unite(t, t->l, t->r);
}
item get(pitem &t, long long l, long long r, long long pl, long long pr) {
  if (!t) return item(0, 0, NULL, NULL);
  if (pl > pr) return item(0, 0, NULL, NULL);
  if (pr < l || r < pl) return item(0, 0, NULL, NULL);
  if (pl <= l && r <= pr) return *t;
  long long lr = (l + r) >> 1;
  item l_it = get(t->l, l, lr, pl, pr);
  item r_it = get(t->r, lr + 1, r, pl, pr);
  item it = item(0, 0, NULL, NULL);
  unite(&it, &l_it, &r_it);
  return it;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> d;
  for (int i = 0; i < n; i++) cin >> a[i];
  for (int i = 0; i < n; i++) {
    long long min_height = a[i] - d;
    long long max_height = a[i] + d;
    item it_l = get(root, 1ll, 1000000000000000ll, 1, min_height);
    item it_r =
        get(root, 1ll, 1000000000000000ll, max_height, 1000000000000000ll);
    item it = item(0, 0, NULL, NULL);
    unite(&it, &it_l, &it_r);
    upd(root, 1ll, 1000000000000000ll, a[i], it.count + 1);
    dp[i] = it.count + 1;
  }
  long long ans = 0;
  for (int i = 0; i < n; i++)
    if (ans < dp[i]) ans = dp[i];
  ans++;
  long long height = 1000000000000000000ll;
  vector<int> ind;
  for (int i = n - 1; i >= 0; i--) {
    if (llabs(a[i] - height) < d) continue;
    if (dp[i] + 1 != ans) continue;
    ind.push_back(i + 1);
    height = a[i];
    ans = dp[i];
  }
  cout << ind.size() << endl;
  for (int i = (int)ind.size() - 1; i >= 0; i--) cout << ind[i] << " ";
  return 0;
}
