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 com.sun.org.apache.xerces.internal.impl.dv.xs.IntegerDV;
import com.sun.org.apache.xerces.internal.impl.xpath.regex.Match;

import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;


public class Main {
    MyScanner cin = new MyScanner(System.in);
    PrintWriter cout = new PrintWriter(System.out);

    int inf = (int) 2e9;
    int N = (int) 1e5;

    private void run() throws FileNotFoundException {
        //MyScanner cin = new MyScanner(new FileReader("strange.in"));
        //PrintWriter cout = new PrintWriter(new File("strange.out"));
        int n = cin.nextInt(), k = cin.nextInt();

        k--;
        int[][] a = new int[n][n];
        long res = 0;

        int cur = 1;

        for (int i = 0; i < n; i++){
            for (int j = 0; j < k; j++){
                a[i][j] = cur++;
            }
        }

        for (int i = 0; i < n; i++){
            for (int j = k; j < n; j++){
                a[i][j] = cur++;
                if (j == k) res += a[i][j];
            }
        }

        cout.println(res);
        for (int i = 0; i < n; i++){
            for (int j = 0; j < n; j++){
                cout.print(a[i][j] + " ");
            }
            cout.print('\n');
        }
        cout.close();
    }

    public static void main(String[] args) throws FileNotFoundException {
        new Main().run();
    }

    class MyScanner {
        BufferedReader br;
        StringTokenizer st;
        public MyScanner(FileReader in){
            br = new BufferedReader(in);
        }
        public MyScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

        String next(){
            while(st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        String tmp = "";
        int nextInt(){return Integer.parseInt(next());}
        double nextDouble(){return Double.parseDouble(next());}
        long nextLong(){return Long.parseLong(next());}

        String nextLine(){
            String str = "";
            try{
                str = br.readLine();
            } catch (IOException e){
                e.printStackTrace();
            }
            return str;
        }
    }
}