Problem: People do many crazy things to stand out in a crowd. Some of them dance, some learn by heart rules of Russian language, some try to become an outstanding competitive programmers, while others collect funny math objects.

Alis is among these collectors. Right now she wants to get one of k-special tables. In case you forget, the table n × n is called k-special if the following three conditions are satisfied:

  * every integer from 1 to n2 appears in the table exactly once; 
  * in each row numbers are situated in increasing order; 
  * the sum of numbers in the k-th column is maximum possible. 



Your goal is to help Alice and find at least one k-special table of size n × n. Both rows and columns are numbered from 1 to n, with rows numbered from top to bottom and columns numbered from left to right.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 500, 1 ≤ k ≤ n) — the size of the table Alice is looking for and the column that should have maximum possible sum.

Output

First print the sum of the integers in the k-th column of the required table.

Next n lines should contain the description of the table itself: first line should contains n elements of the first row, second line should contain n elements of the second row and so on.

If there are multiple suitable table, you are allowed to print any.

Examples

Input

4 1


Output

28
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16


Input

5 3


Output

85
5 6 17 18 19
9 10 23 24 25
7 8 20 21 22
3 4 14 15 16
1 2 11 12 13

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class SP{  
      
      static int mod=1000000007;
      public static void main(String[] args){ 
                  
              int n = intt();
              int k = intt();
              int a[][] = new int[n][n];
               int sum=0,num=n*n;

             for(int i=n-1;i>=0;i--)
               for(int j=n-1;j>=(k-1);j--){

                      a[i][j] = num--;
                      if(j==(k-1))
                         sum = sum+a[i][j];
                }
                  num=1;
              for(int i=0;i<n;i++)
                for(int j=0;j<(k-1);j++)
                    a[i][j]=num++;
                out.println(sum);
 
               for(int i=0;i<n;i++){

                   for(int j=0;j<n;j++)
                        out.print(a[i][j]+" ");
                        out.println("");
                }
             out.flush();
    } 

         static FastReader sc=new FastReader();
         static PrintWriter out = new PrintWriter(System.out);
            static int intt(){
                       int x = sc.nextInt();
                       return(x);
                }
               static long longg(){
                          long x = sc.nextLong();
                           return(x);
                }
               static double doublee(){
                          double t = sc.nextDouble();
                           return(t);
                }
              static String str(){
                       String s = sc.next();
                         return(s);
                }
              static String strln(){

                        String s = sc.nextLine();
                           return(s);
              }
              static long pow(long a,long b){
                       long ans=1;
                      while(b>0){
                          if(b%2==1)
                              ans=(ans*a);
                              a=(a*a)%mod;
                              b=b/2;
                      }
                    return(ans);
                }
           
            static long LCM(long a,long b){
                         return ((a*b)/GCD(a,b));
               }
               static long GCD(long a,long b){
                          
                           if(b%a==0)
                              return(a);
                              return(GCD(b%a,a));
              }

                static long abs(long x,long y)
                   { return(Math.abs(x-y));}

              static long min(long x,long y){
                     return(Math.min(x,y));
                 }

              static long max(long a,long b){
                        return Math.max(a,b);
                  } 

              static long Fermat(long a,long p){
                           long b = p-2,ans=1;
                            while(b>0){
                                 if(b%2==1)
                                      ans=(ans*a)%p;
                                       a=(a*a)%p;
                                       b=b/2;
                              }
                           return(ans);
                   }
              static void Fact(long a[],long m){
                              a[0]=1;
                           for(int i=1;i<a.length;i++)
                                   a[i]=(i*a[i-1])%m;

                      }
              static void Fact_Inv(long a[],long F[],long m){

                                 int n =a.length;
                                     a[n-1]=Fermat(F[n-1],m);
                                 for(int i=n-2;i>=0;i--)
                                        a[i]=((i+1)*a[i+1])%m;
                        }
               /*static  long d, x, y;
              static void extendedEuclid(long A, long B) {
                            if(B == 0) {
                                  d = A;
                                  x = 1;
                                  y = 0;
                              }
                           else {
                                extendedEuclid(B, A%B);
                                 long temp = x;
                                  x = y;
                                 y = temp - (A/B)*y;
                            }
                     } */
                 /*static class pair implements Comparable<pair>{
                       int x,y;
                      pair(int a,int b){
                             x=a;
                             y=b;
                       }
                     public int compareTo(pair p1)
                           { return((p1.x-p1.y)-(this.x-this.y));}
          
                   public boolean equals(Object obj) {
                         if (this == obj)
                                return true;
                        if (obj == null)
                                return false;
                        if (getClass() != obj.getClass())
                                return false;
                         pair other = (pair) obj;
                          if (x != other.x)
                                  return false;
                          if (y != other.y)
                                  return false;
                            return true;
                      }
                      @Override
                 public int hashCode() {
                      return(x-y);
                   } 
          }   */
   static class FastReader { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
}