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.awt.*;
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class C {

    FastScanner in;
    PrintWriter out;

    public void solve() throws IOException {
        int n = in.nextInt();
        int k = in.nextInt();

        int[][] array = new int[n][n];

        int counter = 0;

        for (int i = 0; i < n; i++) { // переход на следующую строку
            for (int j = 0; j < k - 1; j++) { // элементы столбцов в пределах строки i
                array[i][j] = ++counter;
            }
        }

        for (int i = 0; i < n; i++) { // переход на следующую строку
            for (int j = k - 1; j < n; j++) { // элементы столбцов в пределах строки i
                array[i][j] = ++counter;
            }
        }

        int sum = 0;

        for (int i = 0; i < n; i++) {
            sum += array[i][k - 1];
        }

        out.println(sum);

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

    public void run() {
        try {
            //in  = new FastScanner(new File("choose.in"));
            //out = new PrintWriter(new File("choose.out"));

            in = new FastScanner();
            out = new PrintWriter(System.out);

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

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

        FastScanner(File f) {
            try {
                br = new BufferedReader(new FileReader(f));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        String nextLine() {
            String ret = null;
            try {
                ret = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }

            return ret;
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                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());
        }

        int[] nextIntArray(int size) {
            int[] array = new int[size];

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

            return array;
        }

        long[] nextLongArray(int size) {
            long[] array = new long[size];

            for (int i = 0; i < size; i++) {
                array[i] = nextLong();
            }

            return array;
        }

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

        Point nextIntPoint() {
            int x = nextInt();
            int y = nextInt();
            return new Point(x, y);
        }

        Point[] nextIntPointArray(int size) {
            Point[] array = new Point[size];

            for (int index = 0; index < size; ++index) {
                array[index] = nextIntPoint();
            }

            return array;
        }

        java.util.List<Integer>[] readGraph(int vertexNumber, int edgeNumber, boolean undirected) {
            java.util.List<Integer>[] graph = new java.util.List[vertexNumber];

            for (int index = 0; index < vertexNumber; ++index) {
                graph[index] = new ArrayList<Integer>();
            }

            while (edgeNumber-- > 0) {
                int from = nextInt() - 1;
                int to = nextInt() - 1;

                graph[from].add(to);

                if (undirected)
                    graph[to].add(from);
            }

            return graph;
        }
    }

    public static void main(String[] arg) {
        new C().run();
    }
}