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.util.Scanner;

public class Main {
    public static void main(String[] args) {
        class Edge {
            int to,w,next;
            public Edge () {
                ;
            }

            public Edge(int to, int w, int next) {
                this.to = to;
                this.w = w;
                this.next = next;
            }
        }

        class Graph {
            private int v,e;
            private int[] head;
            private Edge[] edges;

            public void addEdge (int u, int v, int w) {
                edges[e]=new Edge();
                edges[e].to=v;
                edges[e].w=w;
                edges[e].next=head[u];
                head[u]=e;
                e++;
            }

            public Graph () {
                ;
            }

            public Graph(int v, int e, int[] head, Edge[] edges) {
                for (int i=0;i<=v;i++) {
                    head[i]=-1;
                }
                this.v = v;
                this.e = e;
                this.head = head;
                this.edges = edges;
            }

            public Graph(int v, int e) {
                this.v = v;
                this.e = e;
            }

            public int getV() {
                return v;
            }

            public void setV(int v) {
                this.v = v;
            }

            public int getE() {
                return e;
            }

            public void setE(int e) {
                this.e = e;
            }

            public int[] getHead() {
                return head;
            }

            public void setHead(int[] head) {
                this.head = head;
            }

            public Edge[] getEdges() {
                return edges;
            }

            public void setEdges(Edge[] edges) {
                this.edges = edges;
            }
        }

        Scanner sc=new Scanner(System.in);
        int n,m;
        n=sc.nextInt();
        m=sc.nextInt();
        boolean[] vis=new boolean[m+1];
        for (int i=1;i<=n;i++) {
            int s,e;
            s=sc.nextInt();
            e=sc.nextInt();
            for (int j=s;j<=e;j++) {
                vis[j]=true;
            }
        }
        int cnt=0;
        int[] res=new int[m+1];
        for (int i=1;i<=m;i++) {
            if (!vis[i]) {
                cnt++;
                res[cnt]=i;
            }
        }
        System.out.println(cnt);
        if (cnt>0) {
            System.out.print(res[1]);
            for (int i=2;i<=cnt;i++) {
                System.out.print(" "+res[i]);
            }
            System.out.println("");
        }
    }
}