Problem: We have a pyramid with N steps, built with blocks. The steps are numbered 1 through N from top to bottom. For each 1≤i≤N, step i consists of 2i-1 blocks aligned horizontally. The pyramid is built so that the blocks at the centers of the steps are aligned vertically.

<image>

A pyramid with N=4 steps

Snuke wrote a permutation of (1, 2, ..., 2N-1) into the blocks of step N. Then, he wrote integers into all remaining blocks, under the following rule:

* The integer written into a block b must be equal to the median of the three integers written into the three blocks directly under b, or to the lower left or lower right of b.



<image>

Writing integers into the blocks

Afterwards, he erased all integers written into the blocks. Now, he only remembers that the integer written into the block of step 1 was x.

Construct a permutation of (1, 2, ..., 2N-1) that could have been written into the blocks of step N, or declare that Snuke's memory is incorrect and such a permutation does not exist.

Constraints

* 2≤N≤10^5
* 1≤x≤2N-1

Input

The input is given from Standard Input in the following format:


N x


Output

If no permutation of (1, 2, ..., 2N-1) could have been written into the blocks of step N, print `No`.

Otherwise, print `Yes` in the first line, then print 2N-1 lines in addition.

The i-th of these 2N-1 lines should contain the i-th element of a possible permutation.

Examples

Input

4 4


Output

Yes
1
6
3
7
4
5
2


Input

2 1


Output

No

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.util.stream.Collectors;
import java.util.stream.IntStream;

import static java.lang.Math.*;
import static java.lang.String.format;

public class Main {
    public static void main(String[] args) {
        solve();
    }
    final static int INF = Integer.MAX_VALUE>>1;
    final static int MOD = 1_000_000_007;
    final static int[] dx4 = { 0, 1, 0, -1 };
    final static int[] dy4 = { 1, 0, -1, 0 };
    final static int[] dx8 = {0, 1, 1,  1,  0, -1, -1, -1};
    final static int[] dy8 = {1, 1, 0, -1, -1, -1, 0, 1};
    final static Runnable me=()->{};
    public static void solve(){
        //TODO:Solve problem like ***
        Scanner sc=new Scanner();
        int n = sc.nextInt();
        int x = sc.nextInt();
        if (x == 1 || x == 2 * n - 1) {
            put("No");
            return;
        }
        int[] ans = new int[2 * n - 1];
        ans[n - 2] = x - 1;
        ans[n - 1]=x;
        ans[n] = x + 1;
        int idx=0;
        for (int i = 1; i <= 2 * n - 1; i++) {
            if(i==x-1||i==x||i==x+1)continue;
            if(idx==n-2){
                idx = n + 1;
            }
            ans[idx++]=i;
        }
        StringBuilder sb = new StringBuilder();
        sb.append("Yes\n");
        for (int i : ans) {
            sb.append(i);
            sb.append("\n");
        }
        put(sb);

    }

    private static int mid(int a, int b, int c) {
        int[] d = {a, b, c};
        Arrays.sort(d);
        return d[1];
    }
    final private static class Permutation {
        public static int startIndexOfDescendingOrder(int[] p){
            //return i
            //mean p[i-1]<p[i]&&p[i]>p[i+1]>p[i+2]>...>p[p.length]
            for(int i=p.length-2;i>=0;i--){
                if(p[i]-p[i+1]>=0)continue;
                return i+1;
            }
            return 0;
        }
        public static <T> int startIndexOfDescendingOrder(T[] p,Comparator<? super T> comparator){
            //return i
            //mean p[i-1]<p[i]&&p[i]>p[i+1]>p[i+2]>...>p[p.length]
            for(int i=p.length-2;i>=0;i--){
                if(comparator.compare(p[i],p[i+1])>=0)continue;
                return i+1;
            }
            return 0;
        }
        public static <T> int startIndexOfDescendingOrder(List<T> list,Comparator<? super T> comparator){
            //return i
            //mean p[i-1]<p[i]&&p[i]>p[i+1]>p[i+2]>...>p[p.length]
            for(int i=list.size()-2;i>=0;i--){
                if(comparator.compare(list.get(i),list.get(i+1))>=0)continue;
                return i+1;
            }
            return 0;
        }

        public static boolean nextPermutation(int[] p) {
            int firstIndex=startIndexOfDescendingOrder(p);
            if(firstIndex==0)return false;
            int ng=p.length;
            int ok=firstIndex;
            firstIndex--;
            while(Math.abs(ng-ok)>1){
                int mid=(ng+ok)/2;
                if(p[mid]>p[firstIndex]){
                    ok=mid;
                }else{
                    ng=mid;
                }
            }
            int t = p[firstIndex];
            p[firstIndex] = p[ok];
            p[ok] = t;
            //p[firstIndex+1]以降のものを逆にする
            firstIndex++;
            Arrays.sort(p,firstIndex,p.length);
            return true;
        }
        public static <T> boolean nextPermutation(T[] p,Comparator<? super T> comparator){
            int firstIndex=startIndexOfDescendingOrder(p,comparator);
            if(firstIndex==0)return false;
            int ng=p.length;
            int ok=firstIndex;
            firstIndex--;
            while(Math.abs(ng-ok)>1){
                int mid=(ng+ok)/2;
                if(comparator.compare(p[mid],p[firstIndex])>0){
                    ok=mid;
                }else{
                    ng=mid;
                }
            }
            T t = p[firstIndex];
            p[firstIndex] = p[ok];
            p[ok] = t;
            //p[firstIndex+1]以降のものを逆にする
            //現在降順で昇順に並べる
            //ソートのほうが簡潔に書ける
            firstIndex++;
            Arrays.sort(p,firstIndex,p.length);
            return true;
        }
        public static <T> boolean nextPermutation(List<T> list,Comparator<T> comparator) {
            int firstIndex=startIndexOfDescendingOrder(list,comparator);
            if(firstIndex==0)return false;
            int ng=list.size();
            int ok=firstIndex;
            firstIndex--;
            //MGR式
            while(Math.abs(ng-ok)>1){
                int mid=(ng+ok)/2;
                if(comparator.compare(list.get(mid),list.get(firstIndex))>0){
                    //真に大きいならokの領域
                    ok=mid;
                }else{
                    ng=mid;
                }
            }
            T t = list.get(firstIndex);
            list.set(firstIndex,list.get(ok));
            list.set(ok,t);
            //インデックスがfirstIndex+1以降のものを逆にする
            firstIndex++;
            Collections.reverse(list.subList(firstIndex,list.size()));
            return true;
        }
        public static <T> boolean prevPermutation(List<T> list,Comparator<T> comparator){
            return nextPermutation(list,comparator.reversed());
        }
    }
    //runWhenEAで使う
    private static Runnable func(Object... objects){
        try{
            assert false;
            return me;
        }catch(AssertionError e){
            return ()->{put(objects);};
        }
    }
    private static void print(Object... objects){
        if(objects.length==1){
            System.out.print(objects[0]);
        }else{
            System.out.print(Arrays.toString(objects));
        }
    }
    private static void put(Object... objects) {
        print(objects);
        put();
    }
    private static void put(){
        System.out.println();
    }


    private static void runWhenEA(Runnable runnable){
        try{
            assert false;
        }catch(AssertionError e){
            PrintStream ps=System.out;
            PrintStream pse=System.err;
            System.setOut(pse);
            runnable.run();
            System.setOut(ps);
        }
    }
    private static void putM(String name,char[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,int[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,long[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    private static void putM(String name,boolean[][] mat){
        put("---------------------"+name+"-----------------");
        for (int i = 0; i < mat.length; i++) {
            put(Arrays.toString(mat[i]));
        }
    }
    final static private class Scanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte())
                return buffer[ptr++];
            else
                return -1;
        }

        private boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        public boolean hasNext() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr]))
                ptr++;
            return hasNextByte();
        }

        public String next() {
            if (!hasNext())
                throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            if (!hasNext())
                throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while (true) {
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                } else if (b == -1 || !isPrintableChar(b)) {
                    return minus ? -n : n;
                } else {
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }

        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
                throw new NumberFormatException();
            return (int) nl;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
    final static private class FixedIntPair {
        final public int x, y;
        final static public FixedIntPair ZEROS=new FixedIntPair(0,0);
        FixedIntPair(int x, int y) {
            this.x = x;
            this.y = y;
        }
        public static double distance(FixedIntPair fip1,FixedIntPair fip2){
            double x = (double) fip1.x - fip2.x;
            double y = (double) fip1.y - fip2.y;
            return Math.sqrt(x*x+y*y);
        }

        @Override
        public int hashCode() {
            return x*100000+y;
        }

        @Override
        public boolean equals(Object obj) {
            if(obj==null)return false;
            if(!(obj instanceof FixedIntPair)) return false;
            FixedIntPair pair=(FixedIntPair) obj;
            return this.x==pair.x&&this.y==pair.y;
        }

        @Override
        public String toString() {
            return format(FixedIntPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class FixedLongPair {
        final public long x, y;
        final static public FixedLongPair ZEROS=new FixedLongPair(0,0);
        FixedLongPair(long x, long y) {
            this.x = x;
            this.y = y;
        }
        public static double distance(FixedLongPair flp1,FixedLongPair flp2){
            double x = (double) flp1.x - flp2.x;
            double y = (double) flp1.y - flp2.y;
            return Math.sqrt(x*x+y*y);
        }

        @Override
        public int hashCode() {
            return (int)x+(int)y;
        }

        @Override
        public boolean equals(Object obj) {
            if(obj==null)return false;
            if(!(obj instanceof FixedLongPair)) return false;
            FixedLongPair pair=(FixedLongPair)obj;
            return this.x==pair.x&&this.y==pair.y;
        }

        @Override
        public String toString() {
            return format(FixedLongPair.class.getSimpleName()+":(%d,%d)", x, y);
        }
    }
    final static private class Binary{
        public static String toZeroPadding(int i){
            return format("%"+Integer.toBinaryString(-1).length()+"s",Integer.toBinaryString(i)).replace(' ','0');
        }
        public static String toZeroPadding(long i){
            return format("%"+Long.toBinaryString(-1).length()+"s",Long.toBinaryString(i)).replace(' ','0');
        }
    }

    final static private class Util {
        static long gcd(long a,long b){
            a= abs(a);
            b= abs(b);
            if(a<b){
                long tmp=a;
                a=b;
                b=tmp;
            }
            while(b!=0){
                long r=a%b;
                a=b;
                b=r;
            }
            return a;
        }
        static int gcd(int a,int b){
            a= abs(a);
            b= abs(b);
            if(a<b){
                int tmp=a;
                a=b;
                b=tmp;
            }
            while(b!=0){
                int r=a%b;
                a=b;
                b=r;
            }
            return a;
        }
        static long lcm(long a,long b){
            long gcd=gcd(a,b);
            long result=b/gcd;
            return a*result;
        }
        static boolean isValidCell(int i,int j,int h,int w){
            return i>=0&&i<h&&j>=0&&j<w;
        }
    }
}































































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