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.StringTokenizer;

public class Main {

    private static NotMyScanner in;
    private static PrintWriter out;

    private static void solve() throws IOException {
        int n = in.nextInt(), k = in.nextInt() - 1;
        int[][] t = new int[n][n];
        int num = 1;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < k; j++) {
                t[i][j] = num++;
            }
        }
        for (int i = 0; i < n; i++) {
            for (int j = k; j < n; j++) {
                t[i][j] = num++;
            }
        }
        int sum = 0;
        for (int i = 0; i < n; i++) {
            sum += t[i][k];
        }
        out.println(sum);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                out.print(t[i][j] + " ");
            }
            out.println();
        }
    }

    public static void main(String[] args) throws IOException {
        in = new NotMyScanner();
        out = new PrintWriter(System.out, false);
        solve();
        out.close();
    }
}

class NotMyScanner {

    private final BufferedReader br;
    private StringTokenizer st;
    private String last;

    public NotMyScanner() {
        br = new BufferedReader(new InputStreamReader(System.in));
    }

    public NotMyScanner(String path) throws IOException {
        br = new BufferedReader(new FileReader(path));
    }

    public NotMyScanner(String path, String decoder) throws IOException {
        br = new BufferedReader(new InputStreamReader(new FileInputStream(path), decoder));
    }

    String next() throws IOException {
        while (st == null || !st.hasMoreElements())
            st = new StringTokenizer(br.readLine());
        last = null;
        return st.nextToken();
    }

    String nextLine() throws IOException {
        st = null;
        return (last == null) ? br.readLine() : last;
    }

    boolean hasNext() {
        if (st != null && st.hasMoreElements())
            return true;

        try {
            while (st == null || !st.hasMoreElements()) {
                last = br.readLine();
                st = new StringTokenizer(last);
            }
        } catch (Exception e) {
            return false;
        }

        return true;
    }

    String[] nextStrings(int n) throws IOException {
        String[] arr = new String[n];
        for (int i = 0; i < n; i++)
            arr[i] = next();
        return arr;
    }

    String[] nextLines(int n) throws IOException {
        String[] arr = new String[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextLine();
        return arr;
    }

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

    int[] nextInts(int n) throws IOException {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextInt();
        return arr;
    }

    Integer[] nextIntegers(int n) throws IOException {
        Integer[] arr = new Integer[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextInt();
        return arr;
    }

    int[][] next2Ints(int n, int m) throws IOException {
        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;
    }

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

    long[] nextLongs(int n) throws IOException {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextLong();
        return arr;
    }

    long[][] next2Longs(int n, int m) throws IOException {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                arr[i][j] = nextLong();
        return arr;
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(next().replace(',', '.'));
    }

    double[] nextDoubles(int size) throws IOException {
        double[] arr = new double[size];
        for (int i = 0; i < size; i++)
            arr[i] = nextDouble();
        return arr;
    }

    boolean nextBool() throws IOException {
        String s = next();
        if (s.equalsIgnoreCase("true") || s.equals("1"))
            return true;

        if (s.equalsIgnoreCase("false") || s.equals("0"))
            return false;

        throw new IOException("Boolean expected, String found!");
    }
}