Problem: Valery is a PE teacher at a school in Berland. Soon the students are going to take a test in long jumps, and Valery has lost his favorite ruler! 

However, there is no reason for disappointment, as Valery has found another ruler, its length is l centimeters. The ruler already has n marks, with which he can make measurements. We assume that the marks are numbered from 1 to n in the order they appear from the beginning of the ruler to its end. The first point coincides with the beginning of the ruler and represents the origin. The last mark coincides with the end of the ruler, at distance l from the origin. This ruler can be repesented by an increasing sequence a1, a2, ..., an, where ai denotes the distance of the i-th mark from the origin (a1 = 0, an = l).

Valery believes that with a ruler he can measure the distance of d centimeters, if there is a pair of integers i and j (1 ≤ i ≤ j ≤ n), such that the distance between the i-th and the j-th mark is exactly equal to d (in other words, aj - ai = d). 

Under the rules, the girls should be able to jump at least x centimeters, and the boys should be able to jump at least y (x < y) centimeters. To test the children's abilities, Valery needs a ruler to measure each of the distances x and y. 

Your task is to determine what is the minimum number of additional marks you need to add on the ruler so that they can be used to measure the distances x and y. Valery can add the marks at any integer non-negative distance from the origin not exceeding the length of the ruler.

Input

The first line contains four positive space-separated integers n, l, x, y (2 ≤ n ≤ 105, 2 ≤ l ≤ 109, 1 ≤ x < y ≤ l) — the number of marks, the length of the ruler and the jump norms for girls and boys, correspondingly.

The second line contains a sequence of n integers a1, a2, ..., an (0 = a1 < a2 < ... < an = l), where ai shows the distance from the i-th mark to the origin.

Output

In the first line print a single non-negative integer v — the minimum number of marks that you need to add on the ruler.

In the second line print v space-separated integers p1, p2, ..., pv (0 ≤ pi ≤ l). Number pi means that the i-th mark should be at the distance of pi centimeters from the origin. Print the marks in any order. If there are multiple solutions, print any of them.

Examples

Input

3 250 185 230
0 185 250


Output

1
230


Input

4 250 185 230
0 20 185 250


Output

0


Input

2 300 185 230
0 300


Output

2
185 230

Note

In the first sample it is impossible to initially measure the distance of 230 centimeters. For that it is enough to add a 20 centimeter mark or a 230 centimeter mark.

In the second sample you already can use the ruler to measure the distances of 185 and 230 centimeters, so you don't have to add new marks.

In the third sample the ruler only contains the initial and the final marks. We will need to add two marks to be able to test the children's skills.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.awt.Point;
import java.math.BigDecimal;
import java.math.BigInteger;

import static java.lang.Math.*;

// Solution is at the bottom of code

public class B implements Runnable{
	
	final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
	
	BufferedReader in;
	OutputWriter out;
	StringTokenizer tok = new StringTokenizer("");
	
	public static void main(String[] args){
		new Thread(null, new B(), "", 128 * (1L << 20)).start();
	}
	
	/////////////////////////////////////////////////////////////////////
	
	void init() throws FileNotFoundException{
		Locale.setDefault(Locale.US);
		
		if (ONLINE_JUDGE){
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new OutputWriter(System.out);
		}else{
			in = new BufferedReader(new FileReader("input.txt"));
			out = new OutputWriter("output.txt");
		}
	}
	
	////////////////////////////////////////////////////////////////
	
	long timeBegin, timeEnd;

	void time(){
		timeEnd = System.currentTimeMillis();
		System.err.println("Time = " + (timeEnd - timeBegin));
	}
	
	void debug(Object... objects){
		if (ONLINE_JUDGE){
			for (Object o: objects){
				System.err.println(o.toString());
			}
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	public void run(){
		try{
			timeBegin = System.currentTimeMillis();
			Locale.setDefault(Locale.US);
			
			init();
			solve();
			
			out.close();
			time();
		}catch (Exception e){
			e.printStackTrace(System.err);
			System.exit(-1);
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	String delim = " ";
	
	String readString() throws IOException{
		while(!tok.hasMoreTokens()){
			try{
				tok = new StringTokenizer(in.readLine());
			}catch (Exception e){
				return null;
			}
		}
		
		return tok.nextToken(delim);
	}
	
	String readLine() throws IOException{
		return in.readLine();
	}
	
	/////////////////////////////////////////////////////////////////
	
	final char NOT_A_SYMBOL = '\0';
	
	char readChar() throws IOException{
		int intValue = in.read();
		
		if (intValue == -1){
			return NOT_A_SYMBOL;
		}
		
		return (char) intValue;
	}
	
	char[] readCharArray() throws IOException{
		return readLine().toCharArray();
	}
	
	/////////////////////////////////////////////////////////////////
	
	int readInt() throws IOException {
		return Integer.parseInt(readString());
	}
	
	int[] readIntArray(int size) throws IOException {
		int[] array = new int[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readInt();
		}
		
		return array;
	}
	
	int[] readSortedIntArray(int size) throws IOException {
		Integer[] array = new Integer[size];
		
		for (int index = 0; index < size; ++index) {
			array[index] = readInt();
		}
		Arrays.sort(array);
		
		int[] sortedArray = new int[size];
		for (int index = 0; index < size; ++index) {
			sortedArray[index] = array[index];
		}
		
		return sortedArray;
	}
	
	int[] readIntArrayWithDecrease(int size) throws IOException {
		int[] array = readIntArray(size);
		
		for (int i = 0; i < size; ++i) {
			array[i]--;
		}
		
		return array;
	}
	
	///////////////////////////////////////////////////////////////////
	
	int[][] readIntMatrix(int rowsCount, int columnsCount) throws IOException {
		int[][] matrix = new int[rowsCount][];
		
		for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
			matrix[rowIndex] = readIntArray(columnsCount);
		}
		
		return matrix;
	}
	
	int[][] readIntMatrixWithDecrease(int rowsCount, int columnsCount) throws IOException {
		int[][] matrix = new int[rowsCount][];
		
		for (int rowIndex = 0; rowIndex < rowsCount; ++rowIndex) {
			matrix[rowIndex] = readIntArrayWithDecrease(columnsCount);
		}
		
		return matrix;
	}
	
	///////////////////////////////////////////////////////////////////
	
	long readLong() throws IOException{
		return Long.parseLong(readString());
	}
	
	long[] readLongArray(int size) throws IOException{
		long[] array = new long[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readLong();
		}
		
		return array;
	}
	
	////////////////////////////////////////////////////////////////////
	
	double readDouble() throws IOException{
		return Double.parseDouble(readString());
	}
	
	double[] readDoubleArray(int size) throws IOException{
		double[] array = new double[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readDouble();
		}
		
		return array;
	}
	
	////////////////////////////////////////////////////////////////////
		
	BigInteger readBigInteger() throws IOException {
		return new BigInteger(readString());
	}
	
	BigDecimal readBigDecimal() throws IOException {
		return new BigDecimal(readString());
	}
	
	/////////////////////////////////////////////////////////////////////
	
	Point readPoint() throws IOException{
		int x = readInt();
		int y = readInt();
		return new Point(x, y);
	}
	
	Point[] readPointArray(int size) throws IOException{
		Point[] array = new Point[size];
		
		for (int index = 0; index < size; ++index){
			array[index] = readPoint();
		}
		
		return array;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	List<Integer>[] readGraph(int vertexNumber, int edgeNumber)
	throws IOException{
		@SuppressWarnings("unchecked")
		List<Integer>[] graph = new List[vertexNumber];
		
		for (int index = 0; index < vertexNumber; ++index){
			graph[index] = new ArrayList<Integer>();
		}
		
		while (edgeNumber-- > 0){
			int from = readInt() - 1;
			int to = readInt() - 1;
			
			graph[from].add(to);
			graph[to].add(from);
		}
		
		return graph;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static class IntIndexPair {
		
		static Comparator<IntIndexPair> increaseComparator = new Comparator<B.IntIndexPair>() {
			
			@Override
			public int compare(IntIndexPair indexPair1, IntIndexPair indexPair2) {
				int value1 = indexPair1.value;
				int value2 = indexPair2.value;
				
				if (value1 != value2) return value1 - value2;
				
				int index1 = indexPair1.index;
				int index2 = indexPair2.index;
				
				return index1 - index2;
			}
		};
		
		static Comparator<IntIndexPair> decreaseComparator = new Comparator<B.IntIndexPair>() {
			
			@Override
			public int compare(IntIndexPair indexPair1, IntIndexPair indexPair2) {
				int value1 = indexPair1.value;
				int value2 = indexPair2.value;
				
				if (value1 != value2) return -(value1 - value2);
				
				int index1 = indexPair1.index;
				int index2 = indexPair2.index;
				
				return index1 - index2;
			}
		};
		
		int value, index;

		public IntIndexPair(int value, int index) {
			super();
			this.value = value;
			this.index = index;
		}		
		
		public int getRealIndex() {
			return index + 1;
		}
	}
	
	IntIndexPair[] readIntIndexArray(int size) throws IOException {
		IntIndexPair[] array = new IntIndexPair[size];
		
		for (int index = 0; index < size; ++index) {
			array[index] = new IntIndexPair(readInt(), index);
		}
		
		return array;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static class OutputWriter extends PrintWriter {

		final int DEFAULT_PRECISION = 12;
		
		protected int precision;
		protected String format, formatWithSpace;
		
		{
			precision = DEFAULT_PRECISION;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		public OutputWriter(OutputStream out) {
			super(out);
		}

		public OutputWriter(String fileName) throws FileNotFoundException {
			super(fileName);
		}
		
		public int getPrecision() {
			return precision;
		}

		public void setPrecision(int precision) {
			precision = max(0, precision);
			this.precision = precision;
			
			format = createFormat(precision);
			formatWithSpace = format + " ";
		}
		
		private String createFormat(int precision){
			return "%." + precision + "f";
		}
		
		@Override
		public void print(double d){
			printf(format, d);
		}
		
		public void printWithSpace(double d){
			printf(formatWithSpace, d);
		}

		public void printAll(double...d){
			for (int i = 0; i < d.length - 1; ++i){
				printWithSpace(d[i]);
			}
			
			print(d[d.length - 1]);
		}
		
		@Override
		public void println(double d){
			printlnAll(d);
		}
		
		public void printlnAll(double... d){
			printAll(d);
			println();
		}
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static final int[][] steps = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}}; 
	static final int[][] steps8 = {
			{-1, 0}, {1, 0}, {0, -1}, {0, 1},
			{-1, -1}, {1, 1}, {1, -1}, {-1, 1}
	};
	
	static final boolean check(int index, int lim){
		return (0 <= index && index < lim);
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static final boolean checkBit(int mask, int bit){
		return (mask & (1 << bit)) != 0;
	}
	
	/////////////////////////////////////////////////////////////////////
	
	static final long getSum(int[] array) {
		long sum = 0;
		for (int value: array) {
			sum += value;
		}
		
		return sum;
	}
	
	static final Point getMinMax(int[] array) {
		int min = array[0];
		int max = array[0];
		
		for (int index = 0, size = array.length; index < size; ++index, ++index) {
			int value = array[index];
			
			if (index == size - 1) {
				min = min(min, value);
				max = max(max, value);
			} else {
				int otherValue = array[index + 1];
				
				if (value <= otherValue) {
					min = min(min, value);
					max = max(max, otherValue);
				} else {
					min = min(min, otherValue);
					max = max(max, value);
				}
			}
		}
		
		return new Point(min, max);
	}
	
	/////////////////////////////////////////////////////////////////////
	
	void solve() throws IOException {
		int n = readInt();
		int l = readInt();
		
		int x = readInt();
		int y = readInt();
		
		int[] a = readIntArray(n);
		
		Set<Integer> set = new HashSet<Integer>();
		for (int i = 0; i < n; ++i) {
			set.add(a[i]);
		}
		
		boolean existX = false, existY = false;
		
		Set<Integer> needForX = new HashSet<Integer>();
		Set<Integer> needForY = new HashSet<Integer>();
		
		for (int i = 0; i < n; ++i) {
			int downX = a[i] - x;
			if (check(downX, l)) {
				if (set.contains(downX)) {
					existX = true;
				} else {
					needForX.add(downX);
				}
			}
			
			int upX = a[i] + x;
			if (check(upX, l)) {
				if (set.contains(upX)) {
					existX = true;
				} else {
					needForX.add(upX);
				}
			}
			
			int downY = a[i] - y;
			if (check(downY, l)) {
				if (set.contains(downY)) {
					existY = true;
				} else {
					needForY.add(downY);
				}
			}
			
			int upY = a[i] + y;
			if (check(upY, l)) {
				if (set.contains(upY)) {
					existY = true;
				} else {
					needForY.add(upY);
				}
			}
		}
		
		List<Integer> answer = new ArrayList<Integer>();
		if (existX && existY) {
			
		} else if (existX) {
			for (int i : needForY) {
				answer.add(i);
				break;
			}
		} else if (existY) {
			for (int i : needForX) {
				answer.add(i);
				break;
			}
		} else {
			for (int i : needForX) {
				if (needForY.contains(i)) {
					answer.add(i);
					break;
				}
			}
			
			if (answer.size() == 0) {
				for (int i : needForY) {
					answer.add(i);
					break;
				}
				
				for (int i : needForX) {
					answer.add(i);
					break;
				}
			}
		}
		
		out.println(answer.size());
		for (int i : answer) {
			out.print(i + " ");
		}
		out.println();
	}
}