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.io.*;
import java.math.*;
import java.util.*;

/**
 *
 * @author Saju
 *
 */

public class Main {

    private static int dx[] = { 1, 0, -1, 0 };
    private static int dy[] = { 0, -1, 0, 1 };

    private static final long INF = Long.MAX_VALUE;
    private static final int INT_INF = Integer.MAX_VALUE;
    private static final long NEG_INF = Long.MIN_VALUE;
    private static final int NEG_INT_INF = Integer.MIN_VALUE;
    private static final double EPSILON = 1e-10;

    private static final int MAX = 1000000007;
    
    private static final long MOD = 1000000007;

    private static final int MAXN = 1000000000;
    private static final int MAXA = 100007;
    private static final int MAXLOG = 22;

	public static void main(String[] args) throws IOException {

		InputReader in = new InputReader(System.in);
//		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

//         InputReader in = new InputReader(new FileInputStream("src/test.in"));
//         PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("src/test.out")));

		
		
/*

72 1007 442 1001
0 26 27 64 75 82 103 110 129 133 139 147 165 176 179 200 212 227 248 252 268 276 303 306 317 327 337 344 345 380 387 402 412 433 438 500 518 525 529 531 538 543 574 582 589 600 620 645 677 695 704 725 741 771 772 787 792 803 804 805 806 822 833 882 887 896 899 926 977 984 1001 1007


*/
		
		int n = in.nextInt();
		int l = in.nextInt();
		int x = in.nextInt();
		int y = in.nextInt();
		
		long[] arr = in.nextLongArr(n);
		int cnt = 0;
		
		int upx = upperBound(arr, x);
//		System.out.println(upx);
		int a = -1;
		int b = -1;
		if(arr[upx] != x) {
			for(int i = upx; i < n; i++) {
				long xx = arr[i] - x;
				int upxx = upperBound(arr, xx);
				if(arr[upxx] == xx) {
					a = x;
					break;
				}
			}
			if(a == -1) {
				a = x;
				cnt++;
			}
			else {
				a = -1;
			}
//			long xx = arr[upx] - x;
//			int upxx = upperBound(arr, xx);
//			if(arr[upxx] != xx) {
//				cnt++;
//				a = x;
//			}
 		}
//		System.out.println(cnt + " " + a);
		
		int upy = upperBound(arr, y);
//		System.out.println(upy);
		
		if(arr[upy] != y) {
			
			for(int i = upy; i < n; i++) {
				long yy = arr[i] - y;
				int upyy = upperBound(arr, yy);
				if(arr[upyy] == yy) {
					b = y;
					break;
				}
			}
			
			if(b == -1) {
				b = y;
				cnt++;
			}
			else {
				b = -1;
			}
			
//			long yy = arr[upy] - y;
//			int upyy = upperBound(arr, yy);
//			if(arr[upyy] != yy) {
//				cnt++;
//				b = y;
//			}
 		}
		if(cnt == 0) {
			out.println("0");
		}
		else if(cnt == 1) {
			out.println("1");
			if(a != -1) {
				out.println(a);
			}
			else {
				out.println(b);
			}
		}
		else {
			Set<Long> set = new TreeSet<Long>();
			for(int i = 0; i < n; i++) {
				set.add(arr[i]);
				if(arr[i] + x < l) {
					set.add(arr[i] + x);
				}
				if(arr[i] + y < l) {
					set.add(arr[i] + y);
				}
				if(arr[i] - x > 0) {
					set.add(arr[i] - x);
				}
				if(arr[i] - y > 0) {
					set.add(arr[i] - y);
				}
			}
			
			long ans = -1;
			for(long e : set) {
//				arr1[id++] = e;
				long a1 = e - x;
				long a2 = e - y;
				long a3 = e + x;
				long a4 = e + y;
				boolean xfound = false;
				boolean yfound = false;
				if(a1 >= 0 && a1 <= l) {
					int up = upperBound(arr, a1);
					if(arr[up] == a1) {
						xfound = true;
					}
				}
				
				if(a2 >= 0 && a2 <= l) {
					int up = upperBound(arr, a2);
					if(arr[up] == a2) {
						yfound = true;
					}
				}
				
				
				if(!xfound && a3 >= 0 && a3 <= l) {
					int up = upperBound(arr, a3);
					if(arr[up] == a3) {
						xfound = true;
					}
				}
				
				if(!yfound && a4 >= 0 && a4 <= l) {
					int up = upperBound(arr, a4);
					if(arr[up] == a4) {
						yfound = true;
					}
				}
				if(xfound && yfound) {
					ans = e;
					break;
				}
			}
			if(ans != -1) {
				out.println("1");
				out.println(ans);
			}
			else {
				out.println("2");
				out.println(x + " " + y);
			}

			
			
		}
		
		
		in.close();
		out.flush();
		out.close();
		System.exit(0);
	}
	
	
	private static int upperBound(long arr[], long num) {

		int start = 0;
		int end = arr.length - 1;
		int index = 0;
		int len = arr.length;
		int mid = 0;
		while (true) {
			if (start > end) {
				break;
			}
			mid = (start + end) / 2;
			long val = arr[mid];
			if (val > num) {
				end = mid - 1;
			} else if (val < num) {
				start = mid + 1;
			} else {
				return mid;
			}
		}
		if (arr[mid] < num) {
			return mid + 1;
		}
		return mid;
	}
	
	private static boolean isPalindrome(String str) {
		StringBuilder sb = new StringBuilder();
		sb.append(str);
		String str1 = sb.reverse().toString();
		return str.equals(str1);
	}

	private static String getBinaryStr(int n, int len) {
		String str = Integer.toBinaryString(n);
		int k = str.length();
		for (int i = 1; i <= len - k; i++) {
			str = "0" + str;
		}

		return str;
	}
	
	private static String getBinaryStr(long n, int j) {
		String str = Long.toBinaryString(n);
		int k = str.length();
		for (int i = 1; i <= j - k; i++) {
			str = "0" + str;
		}

		return str;
	}
	
	private static long modInverse(long r) {
		return bigMod(r, MOD - 2, MOD);
	}
	
	private static long bigMod(long n, long k, long m) {

        long ans = 1;
        while (k > 0) {
            if ((k & 1) == 1) {
                ans = (ans * n) % m;
            }
            n = (n * n) % m;
            k >>= 1;
        }
        return ans;
    }
    
	private static long ceil(long n, long x) {
		long div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
	}
	
    private static int ceil(int n, int x) {
        int div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
    }

    
    private static int abs(int x) {
        if (x < 0) {
            return -x;
        }
        return x;
    }

    private static long abs(long x) {
        if(x < 0) {
            return -x;
        }
        return x;
    }

    private static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }

    private static int gcd(int a, int b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    private static int log(long x, int base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    private static long min(long a, long b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static int min(int a, int b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static long max(long a, long b) {
        if (a < b) {
            return b;
        }
        return a;
    }

    private static int max(int a, int b) {
        if (a < b) {
            return b;
        }
        return a;
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

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

        public String next() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());

                }
            } catch (IOException e) {
                return null;
            }
            return tokenizer.nextToken();
        }

        public String nextLine() {
            String line = null;
            try {
                tokenizer = null;
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }

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

        public boolean hasNext() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());
                }
            } catch (Exception e) {
                return false;
            }
            return true;
        }
        
        public int[] nextIntArr(int n) {
        	int arr[] = new int[n];
    		for(int i = 0; i < n; i++) {
    			arr[i] = nextInt();
    		}
    		return arr;
        }
        
        public long[] nextLongArr(int n) {
        	long arr[] = new long[n];
    		for(int i = 0; i < n; i++) {
    			arr[i] = nextLong();
    		}
    		return arr;
        }
        
        public int[] nextIntArr1(int n) {
        	int arr[] = new int[n + 1];
    		for(int i = 1; i <= n; i++) {
    			arr[i] = nextInt();
    		}
    		return arr;
        }
        
        public long[] nextLongArr1(int n) {
        	long arr[] = new long[n + 1];
    		for(int i = 1; i <= n; i++) {
    			arr[i] = nextLong();
    		}
    		return arr;
        }
       
        public void close() {
        	try {
        		if(reader != null) {
        			reader.close();
        		}
        	}
        	catch(Exception e) {
        		
        	}
        	
        	
        }
    }

}