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.io.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskE solver = new TaskE();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskE {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int minDiff = in.nextInt();
        long[] height = new long[n];
        for (int i = 0; i < n; ++i)
            height[i] = in.nextLong();
        long[] keyHeight = ArrayUtils.sortAndUnique(height);
        BinaryIndexedTree smallTree = new BinaryIndexedTree(keyHeight.length);
        BinaryIndexedTree bigTree = new BinaryIndexedTree(keyHeight.length);
        int[] maxLength = new int[n];
        int[] next = new int[n];
        for (int i = n - 1; i >= 0; --i) {
            {
                int low = 0;
                int high = keyHeight.length - 1;
                while (low < high) {
                    int mid = (low + high) / 2;
                    if (keyHeight[mid] >= height[i] + minDiff)
                        high = mid;
                    else
                        low = mid + 1;
                }
                if (keyHeight[low] >= height[i] + minDiff) {
                    Entry other = bigTree.get(keyHeight.length - low - 1);
                    if (maxLength[i] < other.maxLength + 1) {
                        maxLength[i] = other.maxLength + 1;
                        next[i] = other.first;
                    }
                }
            }
            {
                int low = 0;
                int high = keyHeight.length - 1;
                while (low < high) {
                    int mid = (low + high + 1) / 2;
                    if (keyHeight[mid] <= height[i] - minDiff)
                        low = mid;
                    else
                        high = mid - 1;
                }
                if (keyHeight[low] <= height[i] - minDiff) {
                    Entry other = smallTree.get(low);
                    if (maxLength[i] < other.maxLength + 1) {
                        maxLength[i] = other.maxLength + 1;
                        next[i] = other.first;
                    }
                }
            }
            Entry entry = new Entry(maxLength[i], i);
            int pos = Arrays.binarySearch(keyHeight, height[i]);
            smallTree.update(pos, entry);
            bigTree.update(keyHeight.length - pos - 1, entry);
        }
        int start = 0;
        for (int i = 0; i < n; ++i)
            if (maxLength[i] > maxLength[start])
                start = i;
        out.println(maxLength[start]);
        while (start != -1) {
            out.print(start + 1);
            out.print(' ');
            start = next[start];
        }
    }

    class Entry implements Comparable<Entry> {
        int maxLength;
        int first;

        Entry(int maxLength, int first) {
            this.maxLength = maxLength;
            this.first = first;
        }

        Entry() {
            this(0, -1);
        }

        public int compareTo(Entry entry) {
            return maxLength - entry.maxLength;
        }
    }

    class BinaryIndexedTree {
        private final Entry[] data;

        BinaryIndexedTree(int n) {
            data = new Entry[n];
            for (int i = 0; i < n; ++i)
                data[i] = new Entry();
        }

        void update(int at, Entry by) {
            while (at < data.length) {
                if (data[at].compareTo(by) < 0)
                    data[at] = by;
                at |= at + 1;
            }
        }

        Entry get(int at) {
            Entry best = new Entry();
            while (at >= 0) {
                if (best.compareTo(data[at]) < 0)
                    best = data[at];
                at -= ~at & (at + 1);
            }
            return best;
        }
    }
}

class InputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public InputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream), 32768);
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens())
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

}

class ArrayUtils {

    public static long[] sortAndUnique(long[] a) {
        Long[] b = new Long[a.length];
        for (int i = 0; i < a.length; ++i)
            b[i] = a[i];
        Arrays.sort(b);
        long[] c = new long[a.length];
        int n = 0;
        for (int i = 0; i < a.length; ) {
            int j = i;
            while (j < a.length && b[i].equals(b[j])) ++j;
            c[n++] = b[i];
            i = j;
        }
        return Arrays.copyOf(c, n);
    }
}

