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 long long N = 2e5 + 5;
long long n, a[N], b[N], d;
vector<long long> zz;
pair<long long, long long> it[N << 2];
long long trace[N];
void upd(long long i, long long l, long long r, long long pos, long long val,
         long long id) {
  if (pos < l || pos > r) return;
  if (l == r) {
    it[i] = make_pair(val, id);
    return;
  }
  long long m = l + (r - l) / 2;
  upd(i << 1, l, m, pos, val, id);
  upd(i << 1 | 1, m + 1, r, pos, val, id);
  it[i] = max(it[i << 1], it[i << 1 | 1]);
}
pair<long long, long long> que(long long i, long long l, long long r,
                               long long u, long long v) {
  if (v < l || u > r || u > v) return make_pair(0, 0);
  if (u <= l && r <= v) return it[i];
  long long m = l + (r - l) / 2;
  return max(que(i << 1, l, m, u, v), que(i << 1 | 1, m + 1, r, u, v));
}
int32_t main() {
  ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
  if (fopen("classi"
            ".in",
            "r"))
    freopen(
        "classi"
        ".in",
        "r", stdin);
  cin >> n >> d;
  for (long long i = 1, __c = n; i <= __c; ++i) cin >> a[i];
  for (long long i = 1, __c = n; i <= __c; ++i) zz.push_back(a[i]);
  sort(begin(zz), end(zz));
  zz.erase(unique(begin(zz), end(zz)), end(zz));
  for (long long i = 1, __c = n; i <= __c; ++i)
    b[i] = lower_bound(begin(zz), end(zz), a[i]) - begin(zz) + 1;
  for (long long i = 1, __c = n; i <= __c; ++i) {
    long long lex = upper_bound(begin(zz), end(zz), a[i] - d) - begin(zz);
    long long rex = lower_bound(begin(zz), end(zz), a[i] + d) - begin(zz) + 1;
    auto now = que(1, 1, n, 1, lex);
    now = max(now, que(1, 1, n, rex, n));
    upd(1, 1, n, b[i], now.first + 1, i);
    trace[i] = now.second;
  }
  cout << it[1].first << '\n';
  long long now = it[1].second;
  vector<long long> path;
  while (now) path.push_back(now), now = trace[now];
  reverse(begin(path), end(path));
  for (auto &v : path) cout << v << ' ';
}
