Problem: There is an infinite pond that can be represented with a number line. There are n rocks in the pond, numbered from 1 to n. The i-th rock is located at an integer coordinate a_i. The coordinates of the rocks are pairwise distinct. The rocks are numbered in the increasing order of the coordinate, so a_1 < a_2 < ... < a_n.

A robot frog sits on the rock number s. The frog is programmable. It has a base jumping distance parameter d. There also is a setting for the jumping distance range. If the jumping distance range is set to some integer k, then the frog can jump from some rock to any rock at a distance from d - k to d + k inclusive in any direction. The distance between two rocks is an absolute difference between their coordinates.

You are assigned a task to implement a feature for the frog. Given two integers i and k determine if the frog can reach a rock number i from a rock number s performing a sequence of jumps with the jumping distance range set to k. The sequence can be arbitrarily long or empty.

You will be given q testcases for that feature, the j-th testcase consists of two integers i and k. Print "Yes" if the i-th rock is reachable and "No" otherwise.

You can output "YES" and "NO" in any case (for example, strings "yEs", "yes", "Yes" and 'YES"' will be recognized as a positive answer).

Input

The first line contains four integers n, q, s and d (1 ≤ n, q ≤ 2 ⋅ 10^5; 1 ≤ s ≤ n; 1 ≤ d ≤ 10^6) — the number of rocks, the number of testcases, the starting rock and the base jumping distance parameter.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — the coordinates of the rocks. The coordinates of the rocks are pairwise distinct. The rocks are numbered in the increasing order of distance from the land, so a_1 < a_2 < ... < a_n.

Each of the next q lines contains two integers i and k (1 ≤ i ≤ n; 1 ≤ k ≤ 10^6) — the parameters to the testcase.

Output

For each of the testcases print an answer. If there is a sequence of jumps from a rock number s to a rock number i with the jumping distance range set to k, then print "Yes". Otherwise, print "No".

Examples

Input


7 4 4 5
1 5 10 13 20 22 28
4 1
7 2
7 3
3 2


Output


Yes
No
Yes
Yes


Input


10 8 6 11
1 2 4 7 8 9 11 13 19 20
2 13
5 8
8 1
6 15
1 15
2 7
7 6
8 9


Output


Yes
Yes
No
Yes
Yes
Yes
Yes
Yes


Input


6 9 6 6
1 2 4 9 18 19
2 17
1 18
5 4
2 11
5 17
6 8
4 3
3 3
6 6


Output


Yes
Yes
Yes
Yes
Yes
Yes
No
No
Yes


Input


4 1 1 10
1 8 10 19
2 1


Output


Yes

Note

Explanation of the first example:

In the first testcase the destination rock is the same as the starting rock, thus no jumps are required to reach it.

In the second testcase the frog can jump any distance in the range [5 - 2; 5 + 2]. Thus, it can reach rock number 5 (by jumping 7 to the right) and rock number 3 (by jumping 3 to the left). From rock number 3 it can reach rock number 2 (by jumping 5 to the left). From rock number 2 it can reach rock number 1 (by jumping 4 to the left). However, there is no way to reach rock number 7.

In the third testcase the frog can jump any distance in the range [5 - 3; 5 + 3]. Thus, it can reach rock number 7 by jumping to rock 5 first and to 7 afterwards.

The fourth testcase is shown in the explanation for the second testcase.

Solution (in JAVA):

Solution:
 import java.io.*;
import java.util.*;
 
public class F {
	InputStream is;
	FastWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni(), Q = ni(), S = ni()-1, D = ni();
		int[] a = na(n);
 
		int[][] qs = new int[Q][];
		for(int i = 0;i < Q;i++){
			qs[i] = new int[]{ni()-1, ni(), i};
		}
		Arrays.sort(qs, (x, y) -> x[1] - y[1]);
 
		PriorityQueue<int[]> pq = new PriorityQueue<>(
				(x, y) -> Math.abs(D-x[0]) - Math.abs(D-y[0]));
		int[] ls = new int[n];
		int[] rs = new int[n];
		for(int i = 0;i < n;i++){
			int pr = lowerBound(a, a[i] + D);
			rs[i] = pr;
			ls[i] = pr-1;
			if(pr < n)pq.add(new int[]{Math.abs(a[i] - a[pr]), i, pr, 2});
			if(pr > i)pq.add(new int[]{Math.abs(a[i] - a[pr-1]), i, pr-1, 1});
		}
 
		int[] ans = new int[Q];
		DJSet ds = new DJSet(n);
		for(int[] q : qs){
			while(!pq.isEmpty() && Math.abs(D-pq.peek()[0]) <= q[1]){
				int[] cur = pq.poll();
				ds.union(cur[1], cur[2]);
				if(cur[3] == 2) {
					rs[cur[1]] = ++cur[2];
					if(cur[2] == n || cur[1]+1 < n && rs[cur[1]] > ls[cur[1]+1])continue;
				}else{
					ls[cur[1]] = --cur[2];
					if(cur[2] == -1 || cur[1]-1 >= 0 && ls[cur[1]] < rs[cur[1]-1])continue;
				}
				cur[0] = Math.abs(a[cur[1]] - a[cur[2]]);
				pq.add(cur);
			}
			ans[q[2]] = ds.equiv(S, q[0]) ? 1 : -1;
		}
		for(int v : ans){
			out.println(v == 1 ? "Yes" : "No");
		}
	}
 
	public static class DJSet {
		public int[] upper;
 
		public DJSet(int n) {
			upper = new int[n];
			Arrays.fill(upper, -1);
		}
 
		public int root(int x) {
			return upper[x] < 0 ? x : (upper[x] = root(upper[x]));
		}
 
		public boolean equiv(int x, int y) {
			return root(x) == root(y);
		}
 
		public boolean union(int x, int y) {
			x = root(x);
			y = root(y);
			if (x != y) {
				if (upper[y] < upper[x]) {
					int d = x;
					x = y;
					y = d;
				}
				upper[x] += upper[y];
				upper[y] = x;
			}
			return x == y;
		}
 
		public int count() {
			int ct = 0;
			for (int u : upper) if (u < 0) ct++;
			return ct;
		}
 
		public int[][] toBucket() {
			int n = upper.length;
			int[][] ret = new int[n][];
			int[] rp = new int[n];
			for (int i = 0; i < n; i++) if (upper[i] < 0) ret[i] = new int[-upper[i]];
			for (int i = 0; i < n; i++) {
				int r = root(i);
				ret[r][rp[r]++] = i;
			}
			return ret;
		}
	}
 
 
	public static int lowerBound(int[] a, int v){ return lowerBound(a, 0, a.length, v); }
	public static int lowerBound(int[] a, int l, int r, int v)
	{
		if(l > r || l < 0 || r > a.length)throw new IllegalArgumentException();
		int low = l-1, high = r;
		while(high-low > 1){
			int h = high+low>>>1;
			if(a[h] >= v){
				high = h;
			}else{
				low = h;
			}
		}
		return high;
	}
 
 
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new F().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
 
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
 
	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}
 
	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
 
	private int[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}
 
	private int ni() { return (int)nl(); }
 
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
 
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
 
	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;
 
		private FastWriter(){out = null;}
 
		public FastWriter(OutputStream os)
		{
			this.out = os;
		}
 
		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}
 
		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}
 
		public FastWriter write(char c)
		{
			return write((byte)c);
		}
 
		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}
 
		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}
 
		private static int countDigits(int l) {
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}
 
		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}
 
		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}
 
		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}
 
		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}
 
		public FastWriter writeln(char c){
			return write(c).writeln();
		}
 
		public FastWriter writeln(int x){
			return write(x).writeln();
		}
 
		public FastWriter writeln(long x){
			return write(x).writeln();
		}
 
		public FastWriter writeln(double x, int precision){
			return write(x, precision).writeln();
		}
 
		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}
 
		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}
 
		public FastWriter writeln()
		{
			return write((byte)'\n');
		}
 
		public FastWriter writeln(int... xs)
		{
			return write(xs).writeln();
		}
 
		public FastWriter writeln(long... xs)
		{
			return write(xs).writeln();
		}
 
		public FastWriter writeln(char[] line)
		{
			return write(line).writeln();
		}
 
		public FastWriter writeln(char[]... map)
		{
			for(char[] line : map)write(line).writeln();
			return this;
		}
 
		public FastWriter writeln(String s)
		{
			return write(s).writeln();
		}
 
		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}
 
		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}
 
		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}
 
	public void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}
 
	// print ids which are 1
	public void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}
 
	public void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}
 
	public void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}
 
	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}
 
	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}
 
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}