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.util.*;
import java.io.*;
import java.math.*;
public class a{
	
	public static void main( String [] args) throws IOException{
		FastScanner sc=new FastScanner();
		int n=sc.nextInt();
		int k=sc.nextInt()-1;
		int [][] a=new int[n][n];
		int cnt=n*n;
		int sum=0;
		for(int i=0;i<n;i++){
			for(int j=n-1;j>=k;j--){
				a[i][j]=cnt--;
				if(j==k)sum+=a[i][j];
			}
		}
		cnt=1;
		for(int i=n-1;i>=0;i--){
			for(int j=0;j<k;j++){
				a[i][j]=cnt++;
			}
		}

		StringBuilder sb=new StringBuilder("");
		for(int i=0;i<n;i++){
			for(int j=0;j<n;j++){
				sb.append(a[i][j]+" ");
			}sb.append("\n");
		}
		System.out.println(sum);
		System.out.println(sb.toString().trim());

	}
}





















































class FastScanner{	
	 private int BUFFER_SIZE = 1 << 16;
	
	private  DataInputStream din;
	
	private  byte[] buffer;
	
	private int bufferPointer, bytesRead;
	
	public FastScanner() {
		din = new DataInputStream(System.in);
		buffer = new byte[BUFFER_SIZE];
		bufferPointer = bytesRead = 0;
	}

	public FastScanner( String file_name) throws IOException {
		din = new DataInputStream(new FileInputStream(file_name));
		buffer = new byte[BUFFER_SIZE];
		bufferPointer = bytesRead = 0;
    }
    
	public String readLine() throws IOException {
		 byte[] buf = new byte[64];
		int cnt = 0, c;
		while ((c = read()) != -1) {
			if (c == '\n')
				break;
			buf[cnt++] = (byte) c;
		}
		return new String(buf, 0, cnt);
	}
    
    public String next() throws IOException{

		byte c = read();
		while(Character.isWhitespace(c)){
			c = read();
		}
		
		 StringBuilder builder = new StringBuilder();
		builder.append((char)c);
		c = read();
		while(!Character.isWhitespace(c)){
			builder.append((char)c);
			c = read();
		}
		
		return builder.toString();
	}

	public int nextInt() throws IOException {
		int ret = 0;
		byte c = read();
		while (c <= ' ')
			c = read();
		 boolean neg = (c == '-');
		if (neg)
			c = read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');

		if (neg)
			return -ret;
		return ret;
	}
	
	public int[] nextIntArray( int n) throws IOException {
		 int arr[] = new int[n];
		for(int i = 0; i < n; i++){
			arr[i] = nextInt();
		}
		return arr;
	}

	public long nextLong() throws IOException {
		long ret = 0;
		byte c = read();
		while (c <= ' ')
			c = read();
		 boolean neg = (c == '-');
		if (neg)
			c = read();
		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');
		if (neg)
			return -ret;
		return ret;
	}
	
	public long[] nextLongArray( int n) throws IOException {
		 long arr[] = new long[n];
		for(int i = 0; i < n; i++){
			arr[i] = nextLong();
		}
		return arr;
	}

	public char nextChar() throws IOException{
		byte c = read();
		while(Character.isWhitespace(c)){
			c = read();
		}
		return (char) c;	
	}
	
	public double nextDouble() throws IOException {
		double ret = 0, div = 1;
		byte c = read();
		while (c <= ' ')
			c = read();
		 boolean neg = (c == '-');
		if (neg)
			c = read();

		do {
			ret = ret * 10 + c - '0';
		} while ((c = read()) >= '0' && c <= '9');

		if (c == '.') {
			while ((c = read()) >= '0' && c <= '9') {
				ret += (c - '0') / (div *= 10);
			}
		}

		if (neg)
			return -ret;
		return ret;
    }
    
	public double[] nextDoubleArray( int n) throws IOException {
		 double arr[] = new double[n];
		for(int i = 0; i < n; i++){
			arr[i] = nextDouble();
		}
		return arr;
	}

	private void fillBuffer() throws IOException {
		bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
		if (bytesRead == -1)
			buffer[0] = -1;
	}

	private byte read() throws IOException {
		if (bufferPointer == bytesRead)
			fillBuffer();
		return buffer[bufferPointer++];
	}

	public void close() throws IOException {
		if (din == null)
			return;
		din.close();
	}

}