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 int maxn = 300005;
long long d, h[maxn], b[maxn];
int m = 0, n, pre[maxn], dp[maxn];
typedef struct BiT1 {
  int t[maxn];
  void update(int x, int k) {
    for (int i = x; i < maxn; i += (i & (-i))) {
      if (dp[k] > dp[t[i]]) {
        t[i] = k;
      }
    }
  }
  int get(int x) {
    int ret = 0;
    for (int i = x; i > 0; i -= (i & (-i))) {
      if (dp[ret] < dp[t[i]]) ret = t[i];
    }
    return ret;
  }
} BiT1;
typedef struct BiT2 {
  int t[maxn];
  void update(int x, int k) {
    for (int i = x; i > 0; i -= (i & (-i))) {
      if (dp[k] > dp[t[i]]) {
        t[i] = k;
      }
    }
  }
  int get(int x) {
    int ret = 0;
    for (int i = x; i < maxn; i += (i & (-i))) {
      if (dp[ret] < dp[t[i]]) ret = t[i];
    }
    return ret;
  }
} BiT2;
BiT1 T1;
BiT2 T2;
stack<int> S;
int main() {
  cin >> n >> d;
  for (int i = 1; i <= n; i++) {
    scanf("%I64d", &h[i]);
    b[m++] = h[i];
    b[m++] = h[i] + d;
    b[m++] = h[i] - d;
  }
  sort(b, b + m);
  m = unique(b, b + m) - b;
  dp[1] = 1;
  int x = lower_bound(b, b + m, h[1]) - b + 1;
  T1.update(x, 1);
  T2.update(x, 1);
  int l = 1, y1, y2;
  for (int i = 2; i <= n; i++) {
    x = lower_bound(b, b + m, h[i] - d) - b + 1;
    y1 = T1.get(x);
    x = lower_bound(b, b + m, h[i] + d) - b + 1;
    y2 = T2.get(x);
    if (dp[y1] < dp[y2]) swap(y1, y2);
    dp[i] = dp[y1] + 1;
    pre[i] = y1;
    x = lower_bound(b, b + m, h[i]) - b + 1;
    T1.update(x, i);
    T2.update(x, i);
    if (dp[i] > dp[l]) l = i;
  }
  cout << dp[l] << endl;
  for (int i = l; i > 0; i = pre[i]) {
    S.push(i);
  }
  while (!S.empty()) {
    printf("%d ", S.top());
    S.pop();
  }
  printf("\n");
  return 0;
}
