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.*;
import java.util.*;

/**
 *
 * @author Saju
 *
 */




public class Main {

    private static int dx[] = { 1, 0, -1, 0 };
    private static int dy[] = { 0, -1, 0, 1 };
    
    private static int dx1[] = { 1, 1, 0, -1, -1, -1, 0, 1 };
    private static int dy1[] = { 0, -1, -1, -1, 0, 1, 1, 1 };

    private static final long INF = (long) Math.pow(10, 16);
    private static final int INT_INF = Integer.MAX_VALUE;
    private static final long NEG_INF = Long.MIN_VALUE;
    private static final int NEG_INT_INF = Integer.MIN_VALUE;
    private static final double EPSILON = 1e-10;

    private static final long MAX = (long) 1e12;
    
    private static final long MOD = 1000000000;

    private static final int MAXN = 200001;
    private static final int MAXA = 10000004;
    private static final int MAXLOG = 22;
    private static final double PI = Math.acos(-1);
    
    public static void main(String[] args) throws IOException {

        InputReader in = new InputReader(System.in);
//        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

//         InputReader in = new InputReader(new FileInputStream("src/test.in"));
//         PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("src/test.out")));

        
        
/*


*/        
      
        int n = in.nextInt();
        int k = in.nextInt();
        
        int[][] arr = new int[n][n];
        int cnt = 0;
        for(int i = 0; i < n; i++) {
        	for(int j = 0; j < k - 1; j++) {
        		arr[i][j] = ++cnt;
        	}
        }
//        for(int i = 0; i < n; i++) {
//        	System.out.println(Arrays.toString(arr[i]));
//        }
        int sum = 0;
        for(int i = 0; i < n; i++) {
        	for(int j = k - 1; j < n; j++) {
        		arr[i][j] = ++cnt;
        		if(j == k - 1) {
        			sum += arr[i][j];
        		}
        	}
        }
        
//        for(int i = 0; i < n; i++) {
//        	System.out.println(Arrays.toString(arr[i]));
//        }
        
//        System.out.println(sum);
        
        out.println(sum);
        for(int i = 0; i < n; i++) {
        	for(int j = 0; j < n; j++) {
        		out.print(arr[i][j] + " ");
        	}
        	out.println();
        }
        
        
        in.close();
        out.flush();
        out.close();
        System.exit(0);
    }
     
	/*
     * return the number of elements in list that are less than or equal to the val
     */
    private static long upperBound(List<Long> list, long val) {
        int start = 0;
        int len = list.size();
        int end = len - 1;
        int mid = 0;

        while (true) {
            if (start > end) {
                break;
            }
            mid = (start + end) >> 1;
            long v = list.get(mid);
            if (v == val) {
                start = mid;
                while(start < end) {
                    mid = (start + end) >> 1;
                    if(list.get(mid) == val) {
                        if(mid + 1 < len && list.get(mid + 1) == val) {
                            start = mid + 1;
                        }
                        else {
                            return mid + 1;
                        }
                    }
                    else {
                        end = mid - 1;
                    }
                }
                return start + 1;
            }
            if (v > val) {
                end = mid - 1;
            } else {
                start = mid + 1;
            }
        }
        if (list.get(mid) < val) {
            return mid + 1;
        }
        return mid;
    }


    private static boolean isPalindrome(String str) {
        StringBuilder sb = new StringBuilder();
        sb.append(str);
        String str1 = sb.reverse().toString();
        return str.equals(str1);
    }

    private static String getBinaryStr(long n, int j) {
        String str = Long.toBinaryString(n);
        int k = str.length();
        for (int i = 1; i <= j - k; i++) {
            str = "0" + str;
        }

        return str;
    }
    
    private static long modInverse(long r) {
        return bigMod(r, MOD - 2, MOD);
    }
    
    private static long bigMod(long n, long k, long m) {

        long ans = 1;
        while (k > 0) {
            if ((k & 1) == 1) {
                ans = (ans * n) % m;
            }
            n = (n * n) % m;
            k >>= 1;
        }
        return ans;
    }
    
    private static long ceil(long n, long x) {
        long div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
    }
    
    private static int ceil(int n, int x) {
        int div = n / x;
        if(div * x != n) {
            div++;
        }
        return div;
    }

    
    private static int abs(int x) {
        if (x < 0) {
            return -x;
        }
        return x;
    }
    
    private static double abs(double x) {
        if (x < 0) {
            return -x;
        }
        return x;
    }

    private static long abs(long x) {
        if(x < 0) {
            return -x;
        }
        return x;
    }
    
    private static long lcm(long a, long b) {
        return (a * b) / gcd(a, b);
    }

    private static int lcm(int a, int b) {
        return (a * b) / gcd(a, b);
    }

    private static int gcd(int a, int b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }
    
    private static long gcd(long a, long b) {
        if (a == 0)
            return b;
        return gcd(b % a, a);
    }

    private static int log(long x, int base) {
        return (int) (Math.log(x) / Math.log(base));
    }

    private static int log(long x, long base) {
        return (int) (Math.log(x) / Math.log(base));
    }
    
    private static long min(long a, long b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static int min(int a, int b) {
        if (a < b) {
            return a;
        }
        return b;
    }

    private static long max(long a, long b) {
        if (a < b) {
            return b;
        }
        return a;
    }

    private static int max(int a, int b) {
        if (a < b) {
            return b;
        }
        return a;
    }

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

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
            tokenizer = null;
        }

        public List<Integer> nextList(int n) {
            List<Integer> list = new ArrayList<>();
            for(int i = 0; i < n; i++) {
                list.add(nextInt());
            }
            return list;
        }
        
        public List<Long> nextLongList(int n) {
            List<Long> list = new ArrayList<>();
            for(int i = 0; i < n; i++) {
                list.add(nextLong());
            }
            return list;
        }

        public String next() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());

                }
            } catch (IOException e) {
                return null;
            }
            return tokenizer.nextToken();
        }

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

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

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

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

        public boolean hasNext() {
            try {
                while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                    tokenizer = new StringTokenizer(reader.readLine());
                }
            } catch (Exception e) {
                return false;
            }
            return true;
        }
        
        public int[] nextIntArr(int n) {
            int arr[] = new int[n];
            for(int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
        
        public long[] nextLongArr(int n) {
            long arr[] = new long[n];
            for(int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }
        
        public int[] nextIntArr1(int n) {
            int arr[] = new int[n + 1];
            for(int i = 1; i <= n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }
        
        public long[] nextLongArr1(int n) {
            long arr[] = new long[n + 1];
            for(int i = 1; i <= n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }
       
        public void close() {
            try {
                if(reader != null) {
                    reader.close();
                }
            }
            catch(Exception e) {
                
            }
            
            
        }
    }

}