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 Main {

	BufferedReader in;
	StringTokenizer str = null;
	PrintWriter out;
	
	private String next() throws Exception{
		while (str == null || !str.hasMoreElements())
			str = new StringTokenizer(in.readLine());
		return str.nextToken();
	}
	
	private int nextInt() throws Exception{
		return Integer.parseInt(next());
	}
	
	private long nextLong() throws Exception{
		return Long.parseLong(next());
	}
	
	private double nextDouble() throws Exception{
		return Double.parseDouble(next());
	}

	SegmentTree tree;
	int []dp, prev;

	public void run() throws Exception{
		in =  new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		
		int n = nextInt(), d = nextInt();
		long []a = new long[n];
		for(int i = 0; i < n; ++i) {
			a[i] = nextLong();
		}
		long []b = a.clone();
		Arrays.sort(b);

		tree = new SegmentTree(n);

		dp = new int[n];
		Arrays.fill(dp, 1);
		prev = new int[n];
		Arrays.fill(prev, -1);

		for(int i = 0; i < n; ++i) {
			int lo = -1, hi = n;
			while(hi - lo > 1) {
				int m = lo + (hi - lo) / 2;
				if (b[m] <= a[i] - d) {
					lo = m;
				}else {
					hi = m;
				}
			}
			if (lo != -1) {
				Node node = tree.query(0, lo);
				if (node.value != -oo) {
					if (dp[i] < node.value + 1) {
						dp[i] = node.value + 1;
						prev[i] = node.idx;
					}
				}
			}

			lo = -1;
			hi = n;
			while(hi - lo > 1) {
				int m = lo + (hi - lo) / 2;
				if (b[m] >= a[i] + d) {
					hi = m;
				}else {
					lo = m;
				}
			}

			if (hi != n) {
				Node node = tree.query(hi, n - 1);
				if (node.value != -oo) {
					if (dp[i] < node.value + 1) {
						dp[i] = node.value + 1;
						prev[i] = node.idx;
					}
				}
			}

			lo = -1;
			hi = n;
			while(hi - lo > 1) {
				int m = lo + (hi - lo) / 2;
				if (b[m] <= a[i]) {
					lo = m;
				}else {
					hi = m;
				}
			}

			tree.update(lo, dp[i], i);
		}

		int last = -1;
		for(int i = 0; i < n; ++i) {
			if (last == -1 || dp[i] > dp[last]) {
				last = i;
			}
		}

		out.println(dp[last]);
		List<Integer> ans = new ArrayList<Integer>();
		while(last != -1) {
			ans.add(last + 1);
			last = prev[last];
		}
		Collections.reverse(ans);
		for(int i : ans) {
			out.print(i + " ");
		}
		out.println();
		// out.println(Arrays.toString(dp));
		// out.println(Arrays.toString(prev));

		out.close();
	}

	final static int oo = Integer.MAX_VALUE / 2;

	class SegmentTree {
		Node []tree;
		int n;

		public SegmentTree(int n) {
			this.n = n;
			int N = Integer.highestOneBit(n) << 2;
			tree = new Node[N];
			build(1, 0, n - 1);
		}

		private void build(int v, int tl, int tr) {
			if (tl == tr) {
				tree[v] = new Node(-oo, -1);
				return;
			}
			int tm = (tl + tr) >> 1;
			build(2 * v, tl, tm);
			build(2 * v + 1, tm + 1, tr);

			tree[v] = merge(tree[2 * v], tree[2 * v + 1]);
		}

		public void update(int pos, int val, int idx) {
			update(1, 0, n - 1, pos, val, idx);
		}

		private void update(int v, int tl, int tr, int pos, int val, int idx) {
			if (tl == tr) {
				tree[v].value = val;
				tree[v].idx = idx;
				return;
			}
			int tm = (tl + tr) >> 1;
			if (pos <= tm) {
				update(2 * v, tl, tm, pos, val, idx);
			}else {
				update(2 * v + 1, tm + 1, tr, pos, val, idx);
			}

			tree[v] = merge(tree[2 * v], tree[2 * v + 1]);
		}

		public Node query(int l, int r) {
			return query(1, 0, n - 1, l, r);
		}

		private Node query(int v, int tl, int tr, int l, int r) {
			if (l > r) return new Node(-oo, -1);
			if (tl == l && tr == r) {
				return tree[v];
			}
			int tm = (tl + tr) >> 1;
			Node left = query(2 * v, tl, tm, l, Math.min(tm, r));
			Node right = query(2 * v + 1, tm + 1, tr, Math.max(l, tm + 1), r);

			return merge(left, right);
		}

		private Node merge(Node left, Node right) {
			if (left == null) return right;
			if (right == null) return left;
			if (left.value > right.value) return left;
			return right;
		}
	}
		
	class Node {
		int value, idx;
		public Node(int value, int idx) {
			this.value = value;
			this.idx = idx;
		}
	}
	public static void main(String[] args) throws Exception{
		new Main().run();
	}
}
