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 l[1 << 17], p[1 << 17];
long long a[1 << 17];
stack<int> ans;
int main() {
  int n, d;
  cin >> n >> d;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    l[i] = 1;
    p[i] = -1;
  }
  for (int i = 0; i < n; i++) {
    for (int j = max(0, i - 500); j < i; j++) {
      if (l[j] + 1 > l[i] && abs(a[i] - a[j]) >= d) {
        l[i] = l[j] + 1;
        p[i] = j;
      }
    }
  }
  int t = max_element(l, l + n) - l;
  cout << l[t] << endl;
  while (t > -1) {
    ans.push(t);
    t = p[t];
  }
  while (!ans.empty()) {
    cout << ans.top() + 1 << " ";
    ans.pop();
  }
}
