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.
import java.util.*;
import java.io.*;
public class Solution
{
       static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
    static int getMid(int s, int e)
    {
        return s + (e - s) / 2;
    }
 
    /*
    * A recursive function to get the sum
    of values in given range of the array.
    * The following are parameters 
      for this function.
    *
    * st -> Pointer to segment tree
    * node -> Index of current node in
    *         the segment tree.
    * ss & se -> Starting and ending indexes
    *         of the segment represented
    *         by current node, i.e., st[node]
    * l & r -> Starting and ending indexes
    *         of range query
    */
    static int MaxUtil(int[] st, int ss, 
                       int se, int l,
                       int r, int node)
    {
 
        // If segment of this node is completely
        // part of given range, then return
        // the max of segment
        if (l <= ss && r >= se)
            return st[node];
 
        // If segment of this node does not
        // belong to given range
        if (se < l || ss > r)
            return -1;
 
        // If segment of this node is partially
        // the part of given range
        int mid = getMid(ss, se);
 
        return Math.max(
            MaxUtil(st, ss, mid, l, r,
                     2 * node + 1),
            MaxUtil(st, mid + 1, se, l, r,
                    2 * node + 2));
    }
 
    /*
    * A recursive function to update the
    nodes which have the given index in their
    * range. The following are parameters
    st, ss and se are same as defined above
    * index -> index of the element to be updated.
    */
    static void updateValue(int arr[], int[] 
                            st, int ss,
                            int se, int index, 
                            int value,
                            int node)
    {
        if (index < ss || index > se) {
            System.out.println("Invalid Input");
            return;
        }
 
        if (ss == se) {
 
            // update value in array and in
            // segment tree
            arr[index] = value;
            st[node] = value;
        }
        else {
            int mid = getMid(ss, se);
 
            if (index >= ss && index <= mid)
                updateValue(arr, st, ss, mid, 
                            index, value,
                            2 * node + 1);
            else
                updateValue(arr, st, mid + 1, se, index,
                            value, 2 * node + 2);
 
            st[node] = Math.max(st[2 * node + 1],
                                st[2 * node + 2]);
        }
        return;
    }
 
    // Return max of elements in range from
    // index l (query start) to r (query end).
    static int getMax(int[] st, int n, int l, int r)
    {
 
        // Check for erroneous input values
        if (l < 0 || r > n - 1 || l > r) {
            System.out.printf("Invalid Input\n");
            return -1;
        }
 
        return MaxUtil(st, 0, n - 1, l, r, 0);
    }
 
    // A recursive function that constructs Segment
    // Tree for array[ss..se]. si is index of
    // current node in segment tree st
    static int constructSTUtil(int arr[],
                               int ss, int se,
                               int[] st, int si)
    {
 
        // If there is one element in array, store
        // it in current node of segment tree and return
        if (ss == se) {
            st[si] = arr[ss];
            return arr[ss];
        }
 
        // If there are more than one elements, then
        // recur for left and right subtrees and
        // store the max of values in this node
        int mid = getMid(ss, se);
 
        st[si] = Math.max(
            constructSTUtil(arr, ss, mid,
                            st, si * 2 + 1),
            constructSTUtil(arr, mid + 1,
                            se, st,
                            si * 2 + 2));
 
        return st[si];
    }
 
    /*
    * Function to construct segment tree from
    given array. This function allocates
    * memory for segment tree.
    */
    static int[] constructST(int arr[], int n)
    {
 
        // Height of segment tree
        int x = (int)Math.ceil(Math.log(n) / Math.log(2));
 
        // Maximum size of segment tree
        int max_size = 2 * (int)Math.pow(2, x) - 1;
 
        // Allocate memory
        int[] st = new int[max_size];
 
        // Fill the allocated memory st
        constructSTUtil(arr, 0, n - 1, st, 0);
 
        // Return the constructed segment tree
        return st;
    }
 
    public static void main(String []args) throws IOException
    {
            Reader sc = new Reader();
            int n = sc.nextInt();
            long d = sc.nextLong();
            long h[] = new long[n];
            long temp[] = new long[n];
            for(int i = 0 ; i < n ; i++)
            {
                   h[i] = sc.nextLong();
                   temp[i] = h[i];
            }
            Arrays.sort(temp);
            TreeMap<Long,Integer> map = new TreeMap<Long,Integer>();
            
            for(int i = 0 ; i < n ; i++)
            {
                   if(map.size() == 0)
                   map.put(temp[i],i);
                   
                   else
                   {
                          if(!map.containsKey(temp[i]))
                          map.put(temp[i],map.get(map.lowerKey(temp[i]))+1);
                   }
            }
            int sz = map.size();
            int dp[] = new int[n];
            int pseudo[] = new int[sz];
            int st[] = constructST(pseudo,sz);
            
            int ans = 1;
            for(int i = 0 ; i < n ; i++)
            {
                   int max1 = 0 , max2 = 0;
                   if(map.lowerKey(h[i]-d+1) != null)
                   max1 = getMax(st,sz,0,map.get(map.lowerKey(h[i]-d+1)));
                   
                   if(map.higherKey(h[i]+d-1) != null)
                   max2 = getMax(st,sz,map.get(map.higherKey(h[i]+d-1)),sz-1);
                   
                   dp[i] = Math.max(max1,max2)+1;
                   
                   int pos = map.get(h[i]);
                   updateValue(pseudo,st,0,sz-1,pos,Math.max(pseudo[pos],dp[i]),0);
                   
                   ans = Math.max(ans,dp[i]);
            }
            System.out.println(ans);
            int v[] = new int[ans];
            long last = 10000000000000000L;
            int curr = ans;
            
          /*  for(int i = 0 ; i < n ; i++)
            {
                   System.out.print(dp[i] + " ");
            }
            
            System.out.println();*/
            
            for(int i = n-1 ; i >= 0 ; i--)
            {
                   if(dp[i] == curr && Math.abs(h[i]-last) >= d)
                   {
                          v[--curr] = i+1;
                          last = h[i];
                   }
            }
            
            for(int i = 0 ; i < v.length ; i++)
            {
                   System.out.print(v[i] + " ");
            }
    }
}