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;
long long h[100001] = {0};
long long hops[100001] = {0};
long long previous[100001] = {0};
long long ans[100001] = {0};
int main() {
  int n, d;
  cin >> n >> d;
  int end_point = 1;
  for (int i = 1; i <= n; ++i) {
    cin >> h[i];
    hops[i] = 1;
    for (int j = max(1, i - 500); j < i; j++) {
      if (abs(h[i] - h[j]) >= d && hops[j] + 1 > hops[i]) {
        hops[i] = hops[j] + 1;
        previous[i] = j;
      }
      if (hops[i] > hops[end_point]) {
        end_point = i;
      }
    }
  }
  cout << hops[end_point] << '\n';
  int T = previous[end_point];
  int cnt = 0;
  ans[cnt] = end_point;
  while (T) {
    ans[++cnt] = T;
    T = previous[T];
  }
  for (int i = cnt; i >= 0; i--) {
    cout << ans[i] << " ";
  }
  return 0;
}
