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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Map;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

public class c342 {

	static class Task{		
		
		public void solve(InputReader in, PrintWriter out)
		{
			int n=in.nextInt();
			int k=in.nextInt();
			int mat[][]=new int[n][n];
			int count=1;
			for(int i=0;i<n;i++)
			{
				for(int j=0;j<k-1;j++)
				{
					mat[i][j]=count;
					count++;
				}
			}
			int rev=n*n;
			for(int i=n-1;i>=0;i--)
			{
				for(int j=n-1;j>=k-1;j--)
				{
					mat[i][j]=rev;
					rev--;
				}
			}
			int sum=0;
			for(int i=0;i<n;i++)
			{
				sum+=mat[i][k-1];
			}
			System.out.println(sum);
			joutArray(mat,n,n);
		}
	}
	
	
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in,out);
        out.close();
    }
    
    static int M=1000000000+7;
	static int[] di={1,0,-1,0,1,-1,-1,1};
	static int[] dj={0,1,0,-1,1,1,-1,-1};
    
	static class point{
		int x;int y;
		public point(int x,int y){
			this.x=x;
			this.y=y;
		}
	}
    
    static int abs(int x){if(x>=0)return x;else return -x;}
    static int gcd(int a,int b){return b==0?a:gcd(b,a%b);}
    static int min(int x,int y){return x<y?x:y;}
    static int min(int x,int y,int z){return x<y?(x<z?x:z):(y<z?y:z);}
    static int max(int x,int y){return x>y?x:y;}
    static int max(int x,int y,int z){return x>y?(x>z?x:z):(y>z?y:z);}
    
    static long abs(long x){if(x>=0)return x;else return -x;}
    static long gcd(long a,long b){return b==0?a:gcd(b,a%b);}
    static long min(long x,long y){return x<y?x:y;}
    static long min(long x,long y,long z){return x<y?(x<z?x:z):(y<z?y:z);}
    static long max(long x,long y){return x>y?x:y;}
    static long max(long x,long y,long z){return x>y?(x>z?x:z):(y>z?y:z);}
    
   
    static void joutArray(int arr[]){
    	for(int i=0;i<arr.length;i++){
    		System.out.print(arr[i]+" ");
    	}
    }
    
    static void joutArray(int arr[][],int n,int m){
    	for(int i=0;i<n;i++){
    		for(int j=0;j<m;j++)
    		System.out.print(arr[i][j]+" ");
    		System.out.println();
    	}
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        
        public String nextLine() {
			String fullLine=null;
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					fullLine=reader.readLine();
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
				return fullLine;
			}
			return fullLine;
		}

        public int nextInt() {
            return Integer.parseInt(next());
        }
        
        public long nextLong() {
        	return Long.parseLong(next());
        }
        
        public double nextDouble() {
        	return Double.parseDouble(next());
        }
        
        public int[] nextIntArray(int n) {
        	int arr[]=new int[n];
        	for(int i=0;i<n;i++)
        		arr[i]=nextInt();
        	return arr;
        }
        
        public long[] nextLongArray(int n) {
        	long arr[]=new long[n];
        	for(int i=0;i<n;i++)
        		arr[i]=nextInt();
        	return arr;
        }
        
        public char[] nextCharArray(){
        	char arr[]=next().toCharArray();
        	return arr;
        }
        
        public int[][] nextIntArray(int n,int m){
        	int arr[][]=new int[n][m];
        	for(int i=0;i<n;i++)
        		for(int j=0;j<m;j++)
        			arr[i][j]=nextInt();
        	return arr;
        }
     }
    
}