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.math.BigInteger;
import java.util.StringTokenizer;

public class CF {
    public static void main(String[] args) {
        InputReader inputReader = new InputReader(System.in);
        PrintWriter printWriter = new PrintWriter(System.out, true);

        int n = inputReader.nextInt();
        int k = inputReader.nextInt();

        printWriter.println( (2 * (n * (k - 1) + 1) + (n - k + 1) * (n - 1)) * n / 2);

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < k - 1; j++) {
                printWriter.print((k - 1) * i + j + 1 + " ");
            }
            for (int j = k - 1; j < n ; j++) {
                printWriter.print( n * (k - 1) + (n - k + 1) * i + j + 2 - k + " ");
            }
            printWriter.println();
        }

        printWriter.close();
    }

    private static class InputReader {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        public InputReader(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public int[] nextIntArray(int size) {
            int[] array = new int[size];
            for (int i = 0; i < size; ++i) {
                array[i] = nextInt();
            }
            return array;
        }

        public long[] nextLongArray(int size) {
            long[] array = new long[size];
            for (int i = 0; i < size; ++i) {
                array[i] = nextLong();
            }
            return array;
        }

        public double[] nextDoubleArray(int size) {
            double[] array = new double[size];
            for (int i = 0; i < size; ++i) {
                array[i] = nextDouble();
            }
            return array;
        }

        public String[] nextStringArray(int size) {
            String[] array = new String[size];
            for (int i = 0; i < size; ++i) {
                array[i] = next();
            }
            return array;
        }

        public boolean[][] nextBooleanTable(int rows, int columns, char trueCharacter) {
            boolean[][] table = new boolean[rows][columns];
            for (int i = 0; i < rows; ++i) {
                String row = next();
                assert row.length() == columns;
                for (int j = 0; j < columns; ++j) {
                    table[i][j] = (row.charAt(j) == trueCharacter);
                }
            }
            return table;
        }

        public char[][] nextCharTable(int rows, int columns) {
            char[][] table = new char[rows][];
            for (int i = 0; i < rows; ++i) {
                table[i] = next().toCharArray();
                assert table[i].length == columns;
            }
            return table;
        }

        public int[][] nextIntTable(int rows, int columns) {
            int[][] table = new int[rows][columns];
            for (int i = 0; i < rows; i++) {
                for (int j = 0; j < columns; j++) {
                    table[i][j] = nextInt();
                }
            }
            return table;
        }

        public long[][] nextLongTable(int rows, int columns) {
            long[][] table = new long[rows][columns];
            for (int i = 0; i < rows; i++) {
                for (int j = 0; j < columns; j++) {
                    table[i][j] = nextLong();
                }
            }
            return table;
        }

        public double[][] nextDoubleTable(int rows, int columns) {
            double[][] table = new double[rows][columns];
            for (int i = 0; i < rows; i++) {
                for (int j = 0; j < columns; j++) {
                    table[i][j] = nextDouble();
                }
            }
            return table;
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

        public boolean hasNext() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                String line = readLine();
                if (line == null) {
                    return false;
                }
                tokenizer = new StringTokenizer(line);
            }
            return true;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(readLine());
            }
            return tokenizer.nextToken();
        }

        public String readLine() {
            String line;
            try {
                line = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return line;
        }
    }
}