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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;
import java.util.stream.Collectors;

public class Main {
    private static IO io = new IO();

    public static void main(String[] args) throws Exception {
        int n = io.getInt(), k = io.getInt() - 1, max = 0;
        int[][] mat = new int[n][n];
        int val = n * n;

        for (int i = 0; i < n; i++) {
            for(int j = n - 1 ; j >= k ; j--){
                mat[i][j] = val--;
                if(j == k)
                    max += mat[i][j];
            }
        }
        for (int i = 0; i < n; i++) {
            for(int j = k - 1 ; j >= 0 ; j--){
                mat[i][j] = val--;
            }
        }
        System.out.println(max);
        for(int i = 0 ; i < n ; i++){
            StringJoiner sj = new StringJoiner(" ");
            for(int j = 0 ; j < n ; j++){
                sj.add(String.valueOf(mat[i][j]));
            }
            System.out.println(sj.toString());
        }
    }
}

class IO {
    private BufferedReader br = null;
    private StringTokenizer st = null;

    public IO() {
        this(System.in);
    }

    public IO(InputStream is) {
        this.br = new BufferedReader(new InputStreamReader(is));
    }

    public List<String> getStringArray(int n) throws IOException {
        if (n == 0)
            return new ArrayList<>();
        if (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        List<String> res = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            if (!st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            res.add(st.nextToken());
        }
        return res;
    }

    public String getString() throws IOException {
        List<String> res = this.getStringArray(1);
        return res.size() == 0 ? "" : res.get(0);
    }

    public List<Integer> getIntegerArray(int n) throws IOException {
        if (n == 0)
            return new ArrayList<>();
        List<String> res = getStringArray(n);
        return res.stream().map(Integer::parseInt).collect(Collectors.toList());
    }

    public Integer getInt() throws IOException {
        List<Integer> res = this.getIntegerArray(1);
        return res.size() == 0 ? 0 : res.get(0);
    }

    public List<Long> getLongArray(int n) throws IOException {
        if (n == 0)
            return new ArrayList<>();
        List<String> res = getStringArray(n);
        return res.stream().map(Long::parseLong).collect(Collectors.toList());
    }

    public Long getLong() throws IOException {
        List<Long> res = this.getLongArray(1);
        return res.size() == 0 ? 0L : res.get(0);
    }

    public List<Double> getDoubleArray(int n) throws IOException {
        if (n == 0)
            return new ArrayList<>();
        List<String> res = getStringArray(n);
        return res.stream().map(Double::parseDouble).collect(Collectors.toList());
    }

    public Double getDouble() throws IOException {
        List<Double> res = this.getDoubleArray(1);
        return res.size() == 0 ? 0.0 : res.get(0);
    }
}

class Utils {
    static int[][] fourDirs = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
    static int[][] eightDirs = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}, {1, 1}, {1, -1}, {-1, 1}, {-1, -1}};

    static int modAdd(int a, int b) {
        return (int) ((a + (long) b) % 1000000007);
    }

    static int modSub(int a, int b) {
        return (int) ((a - (long) b + 1000000007) % 1000000007);
    }

    public static List<Integer> sieve(int n) {
        boolean b[] = new boolean[n + 1];
        List<Integer> ans = new ArrayList<>();
        Arrays.fill(b, true);

        for (int i = 2; i <= n; i++) {
            if (b[i]) {
                ans.add(i);
                for (int j = i * i; j >= 0 && j <= n; j += i) {
                    b[j] = false;
                }
            }
        }
        return ans;
    }

    public static boolean isPrime(long n) {
        long sqrt = (long) Math.sqrt(n);
        for (int i = 2; i <= sqrt; i++) {
            if (n % i == 0)
                return false;
        }
        return true;
    }

    public static long mod(long n) {
        if (n > 0)
            return n % 1000000007;
        return (n + 2000000014) % 1000000007;
    }

    public static boolean isSqr(long n) {
        int sqrt = (int) Math.sqrt(n);
        return n == (long) sqrt * sqrt;
    }

    public static boolean inRange(long i, long l, long h) {
        return i >= l && i <= h;
    }

    public static boolean isValid(int i, int j, int n, int m) {
        return i >= 0 && j >= 0 && i < n && j < m;
    }

    public static void swap(List<Integer> ls, int i, int j) {
        int temp = ls.get(i);
        ls.set(i, ls.get(j));
        ls.set(j, temp);
    }

    public static long gcd(long a, long b) {
        if (a < b)
            return gcd(b, a);
        else if (a == b || b == 0)
            return a;
        else {
            return gcd(b, a % b);
        }
    }

    public static long subSum(long[] pre, int l, int h) {
        return l == 0 ? pre[h] : pre[h] - pre[l - 1];
    }

    public static void ifPrint(boolean test, Object ifValue, Object elseValue) {
        System.out.println(test ? ifValue : elseValue);
    }

    public static void print(Character delim, Object... a) {
        List<String> top = new ArrayList<>();
        for (Object aa : a)
            top.add(aa == null ? "null" : aa.toString());
        System.out.println(join(top, delim.toString()));
    }

    public static void print(Object... a) {
        print(' ', a);
    }

    public static <T extends Comparable<T>> int lowerBound(T[] arr, int l, int h, T key) {
        while (l < h) {
            int mid = (l + h) / 2;
            if (arr[mid].compareTo(key) < 0)
                l = mid + 1;
            else
                h = mid;
        }
        return arr[l].compareTo(key) >= 0 ? l : -1;
    }

    public static <T extends Comparable<T>> int upperBound(T[] arr, int l, int h, T key) {
        while (l < h) {
            int mid = (l + h) / 2;
            if (arr[mid].compareTo(key) < 0)
                l = mid + 1;
            else if (arr[mid].compareTo(key) == 0)
                l = mid;
            else
                h = mid;
            if (h == l + 1)
                break;
        }
        return arr[l].compareTo(key) >= 0 ? l : -1;
    }

    public static <T> String join(List<T> ls) {
        return join(ls, " ");
    }

    public static <T> String join(List<T> ls, String delim) {
        StringJoiner sj = new StringJoiner(delim);
        for (T a : ls)
            sj.add(a.toString());
        return sj.toString();
    }

    public static <T> void print2DArray(List<List<T>> mat) {
        for (List<T> m : mat) {
            System.out.println("{ " + join(m, ", ") + " }");
        }
    }

    public static <T> void reverseArrray(T[] arr, int l, int h) {
        while (l < h) {
            T temp = arr[l];
            arr[l] = arr[h];
            arr[h] = temp;
            l++;
            h--;
        }
    }
}