Problem: Roland loves growing flowers. He has recently grown a beautiful rose at point (0, 0) of the Cartesian coordinate system. The rose is so beautiful that Roland is afraid that the evil forces can try and steal it. 

To protect the rose, Roland wants to build n watch towers. Let's assume that a tower is a point on the plane at the distance of at most r from the rose. Besides, Roland assumes that the towers should be built at points with integer coordinates and the sum of squares of distances between all pairs of towers must be as large as possible. Note, that Roland may build several towers at the same point, also he may build some of them at point (0, 0).

Help Roland build the towers at the integer points so that the sum of squares of distances between all towers is maximum possible. Note that the distance in this problem is defined as the Euclidian distance between points.

Input

The first line contains two integers, n and r (2 ≤ n ≤ 8; 1 ≤ r ≤ 30).

Output

In the first line print an integer — the maximum possible sum of squared distances. In the i-th of the following n lines print two integers, xi, yi — the coordinates of the i-th tower. Each tower must be inside or on the border of the circle with radius r. Note that there may be several towers located at the same point of the plane, also some towers can be located at point (0, 0).

If there are multiple valid optimal arrangements, choose any of them.

Examples

Input

4 1


Output

16
0 1
0 1
0 -1
0 -1


Input

3 6


Output

312
0 6
5 -3
-5 -3

Solution (in JAVA):

Solution:
//package round262;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;

public class E2 {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	int[][] hist;
	int W = 35;
	double[][] pps;
	
	void solve()
	{
		int n = ni(), r = ni();
		hist = new int[n][];
		int[][] pps = new int[9000][];
		int p = 0;
		maxd = -1L;
		for(int i = -r;i <= r;i++){
			for(int j = -r;j <= r;j++){
				if(i*i+j*j <= r*r && (r-1)*(r-1) <= i*i+j*j){
					pps[p++] = new int[]{i, j, i*i+j*j};
				}
			}
		}
		Arrays.sort(pps, 0, p, new Comparator<int[]>() {
			public int compare(int[] a, int[] b) {
				return -(a[2] - b[2]);
			}
		});
		long x = 5000000;
		for(int i = 1;i <= n;i++)x *= i;
		pps = Arrays.copyOf(pps, Math.min(p, (int)Math.pow(x, 1./n)));
		dfs(0, n, r, pps, 0);
		
		out.println(maxd);
		for(int[] o : opt){
			out.println(o[0] + " " + o[1]);
		}
	}
	
	long maxd = -1L;
	int gct = 0;
	int[][] opt = null;
	
	void dfs(int pos, int n, int r, int[][] pps, int ind)
	{
		if(pos == n){
			gct++;
			long d = 0;
			for(int i = 0;i < n;i++){
				for(int j = i+1;j < n;j++){
					d += 
							(hist[i][0]-hist[j][0])*(hist[i][0]-hist[j][0]) +
							(hist[i][1]-hist[j][1])*(hist[i][1]-hist[j][1])
							;
				}
			}
			if(d > maxd){
				maxd = d;
//				tr(maxd);
				opt = Arrays.copyOf(hist, n);
			}
			return;
		}
		
		for(int i = ind;i < pps.length;i++){
			hist[pos] = pps[i];
			dfs(pos+1, n, r, pps, i);
		}
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new E2().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}