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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.PriorityQueue;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class div {

	static class SegmentTree { // 1-based DS, OOP

		int N; // the number of elements in the array as a power of 2 (i.e. after padding)
		int[] array;
		pair[] sTree, lazy;

		SegmentTree(int[] in) {
			array = in;
			N = in.length - 1;
			sTree = new pair[N << 1];
			build(1, 1, N);
		}

		void build(int node, int b, int e) // O(n)
		{
			if (b == e)
				sTree[node] = new pair(0, 0);
			else {
				int mid = b + e >> 1;
				build(node << 1, b, mid);
				build(node << 1 | 1, mid + 1, e);
				sTree[node] = new pair(0, 0);
			}
		}

		void update_point(int index, int val, int k) // O(log n)
		{
			index += N - 1;
			sTree[index] = new pair(val, k);
			while (index > 1) {
				index >>= 1;
				if (sTree[index << 1].x > sTree[index << 1 | 1].x)
					sTree[index] = new pair(sTree[index << 1].x, sTree[index << 1].y);
				else
					sTree[index] = new pair(sTree[index << 1 | 1].x, sTree[index << 1 | 1].y);
			}
		}

		pair query(int i, int j) {
			return query(1, 1, N, i, j);
		}

		pair query(int node, int b, int e, int i, int j) // O(log n)
		{
			if (i > e || j < b)
				return new pair(0, 0);
			if (b >= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			// propagate(node, b, mid, e);
			pair q1 = query(node << 1, b, mid, i, j);
			pair q2 = query(node << 1 | 1, mid + 1, e, i, j);
			if (q1.x > q2.x)
				return new pair(q1.x, q1.y);
			return new pair(q2.x, q2.y);

		}

	}

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		long d = Long.parseLong(st.nextToken());
		int N = 1;
		while (N < n)
			N <<= 1;
		long[] a = new long[n];
		long[] b = new long[n];
		HashMap<Long, Integer> hm = new HashMap<>();
		st = new StringTokenizer(br.readLine());
		TreeSet<Long> ts = new TreeSet<>();
		for (int i = 0; i < b.length; i++) {
			Long x = Long.parseLong(st.nextToken());
			a[i] = x;
			b[i] = x;
			ts.add(x);
		}
		Arrays.sort(a);
		for (int i = 1; i <= b.length; i++) {
			hm.put(a[i - 1], i);
		}
		SegmentTree sg = new SegmentTree(new int[N + 1]);
		int[] p = new int[n];
		int max = 0;
		for (int i = 0; i < b.length; i++) {
			int idx = hm.get(b[i]);
			Long num = b[i] - d;
			Long le = ts.floor(num);
			Long ri = ts.ceiling(num + 2 * d);
			pair l = new pair(0, 0);
			if (le != null) {
				l = sg.query(1, hm.get(le));
			}
			pair r = new pair(0, 0);
			if (ri != null)
				r = sg.query(hm.get(ri), N);
			if (l.x > r.x) {
				p[i] = l.y;
				sg.update_point(idx, l.x + 1, i);
			} else {
				if (r.x == 0)
					p[i] = -1;
				else
					p[i] = r.y;
				sg.update_point(idx, r.x + 1, i);
			}

		}
		pair fin = sg.query(1, N);
		Stack<Integer> sta = new Stack<>();
		int i = fin.y;

		while (p[i] != -1) {
			sta.push(i + 1);
			i = p[i];

		}
		sta.push(i + 1);

		pw.println(sta.size());
		while (!sta.isEmpty())
			pw.print(sta.pop() + " ");
		pw.flush();
	}

	static class pair implements Comparable<pair> {
		int x;
		int y;

		public pair(int q, int w) {
			x = q;
			y = w;
		}

		@Override
		public int compareTo(pair o) {
			// TODO Auto-generated method stub
			return x - o.x;
		}
	}

}
