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 n, rez, i, indst, inddr, strt, Prv[100005], Dp[100005], F[2][100005], d;
long long A[100005], B[100005];
int srcst(long long val) {
  int i, rez = 0;
  for (i = 16; i >= 0; i--)
    if (rez + (1 << i) <= n && B[rez + (1 << i)] <= val) rez += (1 << i);
  return rez;
}
int srcdr(long long val) {
  int i, rez = 0;
  for (i = 16; i >= 0; i--)
    if (rez + (1 << i) <= n && B[rez + (1 << i)] < val) rez += (1 << i);
  return (rez + 1);
}
int qryst(int poz) {
  int rez = 0;
  while (poz > 0) {
    if (Dp[rez] < Dp[F[0][poz]]) rez = F[0][poz];
    poz = poz - (poz & (poz ^ (poz - 1)));
  }
  return rez;
}
int qrydr(int poz) {
  int rez = 0;
  while (poz <= n) {
    if (Dp[rez] < Dp[F[1][poz]]) rez = F[1][poz];
    poz = poz + (poz & (poz ^ (poz - 1)));
  }
  return rez;
}
void updst(int poz, int val) {
  while (poz <= n) {
    if (Dp[val] > Dp[F[0][poz]]) F[0][poz] = val;
    poz = poz + (poz & (poz ^ (poz - 1)));
  }
}
void upddr(int poz, int val) {
  while (poz > 0) {
    if (Dp[val] > Dp[F[1][poz]]) F[1][poz] = val;
    poz = poz - (poz & (poz ^ (poz - 1)));
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> d;
  for (i = 1; i <= n; i++) {
    cin >> A[i];
    B[i] = A[i];
  }
  sort(B + 1, B + n + 1);
  for (i = n; i >= 1; i--) {
    indst = qryst(srcst(A[i] - d));
    inddr = qrydr(srcdr(A[i] + d));
    if (Dp[indst] > Dp[inddr]) {
      Dp[i] = 1 + Dp[indst];
      Prv[i] = indst;
    } else {
      Dp[i] = 1 + Dp[inddr];
      Prv[i] = inddr;
    }
    if (Dp[i] > rez) {
      rez = Dp[i];
      strt = i;
    }
    updst(srcst(A[i]), i);
    upddr(srcdr(A[i]), i);
  }
  cout << rez << "\n";
  for (i = 1; i <= rez; i++) {
    cout << strt << " ";
    strt = Prv[strt];
  }
  return 0;
}
