Problem: You are given a set of n segments on the axis Ox, each segment has integer endpoints between 1 and m inclusive. Segments may intersect, overlap or even coincide with each other. Each segment is characterized by two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — coordinates of the left and of the right endpoints. 

Consider all integer points between 1 and m inclusive. Your task is to print all such points that don't belong to any segment. The point x belongs to the segment [l; r] if and only if l ≤ x ≤ r.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 100) — the number of segments and the upper bound for coordinates.

The next n lines contain two integers each l_i and r_i (1 ≤ l_i ≤ r_i ≤ m) — the endpoints of the i-th segment. Segments may intersect, overlap or even coincide with each other. Note, it is possible that l_i=r_i, i.e. a segment can degenerate to a point.

Output

In the first line print one integer k — the number of points that don't belong to any segment.

In the second line print exactly k integers in any order — the points that don't belong to any segment. All points you print should be distinct.

If there are no such points at all, print a single integer 0 in the first line and either leave the second line empty or do not print it at all.

Examples

Input

3 5
2 2
1 2
5 5


Output

2
3 4 


Input

1 7
1 7


Output

0

Note

In the first example the point 1 belongs to the second segment, the point 2 belongs to the first and the second segments and the point 5 belongs to the third segment. The points 3 and 4 do not belong to any segment.

In the second example all the points from 1 to 7 belong to the first segment.

Solution (in JAVA):

Solution:

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

public class Main { 
    
    public static void main(String[] args) throws java.lang.Exception { 
        Reader pm =new Reader(); 
        //Scanner pm = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int t = 1;
        while(t-- > 0){
            int n = pm.nextInt();
            int m = pm.nextInt();

            int[] a = new int[n];
            int[] b = new int[n];

            for(int i=0;i<n;i++) {
                a[i] = pm.nextInt();
                b[i] = pm.nextInt();
            }
            int ans = 0;
            StringBuffer sb = new StringBuffer();
            for(int i=1;i<=m;i++){
                int cnt = 0;
                for(int j=0;j<n;j++) {
                    if(i < a[j] || i > b[j]) 
                        cnt++;
                }
                if(cnt == n) {
                    ans++;
                    sb.append(i+" ");
                }
            }
            System.out.println(ans);
            System.out.println(sb);
        }
        //end of tests
        
    }
    //end of main class

    static int countInRange(int arr[], int n, int x, int y) { 
        // initialize result 
        int count = 0; 
        count = upperIndex(arr, n, y) -  
                lowerIndex(arr, n, x) + 1; 
        return count; 
    } 
    
    
    static int lowerIndex(int arr[], int n, int x) { 
        int l = 0, h = n - 1; 
        while (l <= h)  
        { 
            int mid = (l + h) / 2; 
            if (arr[mid] >= x) 
                h = mid - 1; 
            else
                l = mid + 1; 
        } 
        return l; 
    } 
      
    // function to find last index <= y 
    static int upperIndex(int arr[], int n, int y) { 
        int l = 0, h = n - 1; 
        while (l <= h)  
        { 
            int mid = (l + h) / 2; 
            if (arr[mid] <= y) 
                l = mid + 1; 
            else
                h = mid - 1; 
        } 
        return h; 
    }
    
    public static StringBuilder dec_to_bin(long n) {
        // decimal to binary upto 30 binaries
        if(n==0) {
            StringBuilder str=new StringBuilder("");
            for(int i=0;i<30;i++) {
                str.append("0");
            }
            return str;
        }
        StringBuilder str=new StringBuilder("");
        while(n!=0) {
            str.append(n%2L);
            n/=2L;
        }
        str=str.reverse();
        StringBuilder tmp_str=new StringBuilder("");
        int len=str.length();
        while(len!=30) {
            tmp_str.append("0");
            len++;
        }
        tmp_str.append(str);
        return tmp_str;
    }
    
    private static int binarySearchPM(int[] arr, int key){
        int n = arr.length;
        int mid = -1;
        int begin = 0,end=n;
        while(begin <= end){
            mid = (begin+end) / 2;
            if(mid == n){
                return n;
            }
            if(key < arr[mid]){
                end = mid-1;
            } else if(key > arr[mid]){
                begin = mid+1;
            } else {
                return mid;
            }
        }
        //System.out.println(begin+" "+end);
        return -begin; //expected Index
    }
    
    static class Reader { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    }
}