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.InputMismatchException;

public class Main {
    private static InputReader ir;
    private static OutputWriter ow;

    public static void main(String[] args) throws Exception {
        initS();
        //initF("INPUT.TXT", "OUTPUT.TXT");
        task();
        exit();
    }

    private static void task() throws Exception {
        int n = ir.nextInt(), k = ir.nextInt() - 1;
        int r = n - k;
        int m = n * n - r + 1;
        int ans = 0;
        for (int i = 0; i < n; ++i) {
            ans += m - i * r;
        }
        ow.println(ans);
        //ow.println(m + " " + r);
        int cnt = 0;
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < k; ++j) {
                ow.print(++cnt + " ");
            }
            for (int j = k; j < n; ++j) {
                ow.print((m - r * (n - i - 1) + j - k) + " ");
            }
            ow.println();
        }

    }

    private static void initS() throws IOException {
        ir = new InputReader(System.in);
        ow = new OutputWriter(System.out);
    }

    private static void initF(String inName, String outName) throws IOException {
        ir = new InputReader(new FileInputStream(inName));
        ow = new OutputWriter(new FileOutputStream(outName));
    }

    private static void exit() throws Exception {
        ir.close();
        ow.close();
    }
}


class InputReader implements AutoCloseable {
    private final InputStream in;
    private int capacity;
    private byte[] buffer;
    private int len = 0;
    private int cur = 0;

    public InputReader(InputStream stream) {
        this(stream, 100_000);
    }

    public InputReader(InputStream stream, int capacity) {
        this.in = stream;
        this.capacity = capacity;
        buffer = new byte[capacity];
    }

    private int read() {
        if (cur >= len) {
            try {
                cur = 0;
                len = in.read(buffer, 0, capacity);
                if (len <= 0)
                    return -1;
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }
        return buffer[cur++];
    }

    private boolean isSpace(int c) {
        return c == ' ' || isEscape(c);
    }

    private boolean isEscape(int c) {
        return c == '\n' || c == '\t' || c == '\r' || c == -1;
    }

    private int readSkipSpace() {
        int c;
        do {
            c = read();
        } while (isSpace(c));
        return c;
    }

    int nextInt() {
        int c = readSkipSpace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res = res * 10 + c - '0';
            c = read();
        } while (!isSpace(c));
        res *= sgn;
        return res;
    }

    public long nextLong() {
        int c = readSkipSpace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res = res * 10 + c - '0';
            c = read();
        } while (!isSpace(c));
        res *= sgn;
        return res;
    }

    int nextChar() {
        return readSkipSpace();
    }

    String nextLine() {
        StringBuilder res = new StringBuilder();
        int c = readSkipSpace();
        do {
            res.append((char) (c));
            c = read();
        } while (!isEscape(c));
        return res.toString();
    }

    @Override
    public void close() throws Exception {
        in.close();
    }
}


class OutputWriter implements Flushable, AutoCloseable {
    private byte[] buf;
    private int capacity;
    private int count;
    private OutputStream out;

    public OutputWriter(OutputStream stream) {
        out = stream;
        capacity = 10_000;
        buf = new byte[capacity];
    }

    public OutputWriter(OutputStream stream, int capacity) {
        if (capacity <= 0)
            throw new IllegalArgumentException("capacity <= 0");
        out = stream;
        this.capacity = capacity;
        buf = new byte[capacity];
    }

    public void write(int b) throws IOException {
        if (count >= buf.length)
            flushBuffer();
        buf[count++] = (byte)b;
    }

    public void write(byte[] bytes, int off, int len) throws IOException {
        if (len >= buf.length) {
            flushBuffer();
            out.write(bytes, off, len);
            return;
        }
        if (len > buf.length - count)
            flushBuffer();
        System.arraycopy(bytes, off, buf, count, len);
        count += len;
    }

    public void write(byte[] bytes) throws IOException {
        write(bytes, 0, bytes.length);
    }

    public void print(int i) throws IOException {
        print(String.valueOf(i));
    }

    public void print(long l) throws IOException {
        print(String.valueOf(l));
    }

    public void print(String str) throws IOException {
        write(str.getBytes());
    }

    public void println() throws IOException {
        print("\n");
    }

    public void println(String str) throws IOException {
        print(str);
        print("\n");
    }

    public void println(int i) throws IOException {
        print(i);
        println();
    }

    public void println(long l) throws IOException {
        print(l);
        println();
    }

    public void print(String separator, Object... objects) throws IOException {
        if (objects == null) return;
        for (int i = 0; i < objects.length; ++i) {
            if (i != 0 && separator != null) print(separator);
            print(objects[i].toString());
        }
    }

    private void flushBuffer() throws IOException {
        if (count > 0) {
            out.write(buf, 0, count);
            count = 0;
        }
    }

    @Override
    public void flush() throws IOException {
        flushBuffer();
        out.flush();
    }

    @Override
    public void close() throws Exception {
        flush();
        out.close();
    }
}