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.math.BigInteger;
import java.util.*;


public class GFGMs
{
    static int mod1=(int)(1e9+7);
    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();
        }
        public int[] nextArray(int n) throws IOException
        {
            int[] a=new int[n];
            for(int i=0;i<n;i++)
            {
                a[i]=nextInt();
            }
            return a;
        }
    }

    static boolean primeCheck(int num0)
    {
        boolean b1=true;
        int num01=(int)(Math.sqrt(num0))+1;
        me1: for(int m=2;m<num01;m++)
        {
            if(num0%m==0)
            {
                b1=false;
                break me1;
            }
        }
        if(num0==1 || num0==0)
        {
            b1=false;
        }
        return b1;
    }
    static long pow1(long x, long y, long p)
    {
        // Initialize result
        long res = 1;

        // Update x if it is more
        // than or equal to p
        x = x % p;

        while (y > 0)
        {
            // If y is odd, multiply x
            // with result
            if((y & 1)==1)
                res = (res * x) % p;

            // y must be even now
            // y = y / 2
            y = y >> 1;
            x = (x * x) % p;
        }
        return res;
    }


    static int find(int pos1,char chr1,String str0)
    {
        int num5=-1;
        int len0=str0.length();
        me0: for(int i=pos1;i<len0;i++)
        {
            if(str0.charAt(i)==chr1)
            {
                num5=i;
                break me0;
            }
        }
        return num5;
    }
    static int gcd(int a, int b)
    {
        if (a == 0 || b == 0)
            return 0;
        if (a == b)
            return a;
        if (a > b)
            return gcd(a-b, b);
        return gcd(a, b-a);
    }
    static void insertionSort(int arr[], int n)
    {
        int i, key, j;
        for (i = 1; i < n; i++)
        {
            key = arr[i];
            j = i-1;

            while (j >= 0 && arr[j] > key)
            {
                arr[j+1] = arr[j];
                j = j-1;
            }
            arr[j+1] = key;
            print(arr,n);
        }
    }
    static void print(int arr[], int n)
    {
        for (int i=0; i < n; i++)
        {
            System.out.print(arr[i] + " ");
        }
        System.out.println();
    }
    public static void main(String[] args) throws IOException
    {
        Reader r=new Reader();
        OutputWriter out1=new OutputWriter(System.out);
        int cas1=r.nextInt();
        int num1=r.nextInt();
        int[] arr1=new int[num1];
        int count1=0;
        Arrays.fill(arr1,0);
        while(cas1-->0)
        {
            int num2=r.nextInt();
            num2=num2-1;
            int num3=r.nextInt();
            for(int i=num2;i<num3;i++)
            {
                arr1[i]=1;
            }
        }
        String str1="";
        for(int i=0;i<num1;i++)
        {
            if(arr1[i]!=1)
            {
                str1=str1+(i+1)+" ";
                count1=count1+1;
            }
        }
        out1.print(count1+"\n");
        if(count1!=0)
        {
            out1.print(str1+"");
        }
        out1.close();
    }
}

class OutputWriter{
    BufferedWriter writer;

    public OutputWriter(OutputStream stream){
        writer = new BufferedWriter(new OutputStreamWriter(stream));
    }

    public void print(int i) throws IOException {
        writer.write(i);
    }

    public void print(String s) throws IOException {
        writer.write(s);
    }

    public void print(char []c) throws IOException {
        writer.write(c);
    }
    public  void close() throws IOException {
        writer.close();
    }
}