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 int a[100000];
int before[100000], jump[100000];
void print(int y) {
  if (before[y] >= 0) {
    print(before[y]);
    printf("%d ", before[y]);
  }
}
int main() {
  int n, d;
  scanf("%d%d", &n, &d);
  for (int i = 1; i <= n; i++) {
    scanf("%I64d", &a[i]);
    jump[i] = 1;
    before[i] = -1;
  }
  int answer = 0, checkpoint = 300, end;
  for (int i = 1; i <= n; i++) {
    for (int j = max(1, i - checkpoint); j < i; j++)
      if (abs(a[i] - a[j]) >= d && jump[i] < jump[j] + 1) {
        jump[i] = jump[j] + 1;
        before[i] = j;
      }
    if (jump[i] > answer) {
      answer = jump[i];
      end = i;
    }
  }
  printf("%d\n", answer);
  print(end);
  printf("%d\n", end);
  return 0;
}
