Currently Tiny is learning Computational Geometry. When trying to solve a problem called "The Closest Pair Of Points In The Plane", he found that a code which gave a wrong time complexity got Accepted instead of Time Limit Exceeded.

The problem is the follows. Given n points in the plane, find a pair of points between which the distance is minimized. Distance between (x1, y1) and (x2, y2) is <image>.

The pseudo code of the unexpected code is as follows:
    
    
      
    input n  
    for i from 1 to n  
        input the i-th point's coordinates into p[i]  
    sort array p[] by increasing of x coordinate first and increasing of y coordinate second  
    d=INF        //here INF is a number big enough  
    tot=0  
    for i from 1 to n  
        for j from (i+1) to n  
            ++tot  
            if (p[j].x-p[i].x>=d) then break    //notice that "break" is only to be  
                                                //out of the loop "for j"  
            d=min(d,distance(p[i],p[j]))  
    output d  
    

Here, tot can be regarded as the running time of the code. Due to the fact that a computer can only run a limited number of operations per second, tot should not be more than k in order not to get Time Limit Exceeded.

You are a great hacker. Would you please help Tiny generate a test data and let the code get Time Limit Exceeded?

Input

A single line which contains two space-separated integers n and k (2 ≤ n ≤ 2000, 1 ≤ k ≤ 109).

Output

If there doesn't exist such a data which let the given code get TLE, print "no solution" (without quotes); else print n lines, and the i-th line contains two integers xi, yi (|xi|, |yi| ≤ 109) representing the coordinates of the i-th point.

The conditions below must be held:

  * All the points must be distinct. 
  * |xi|, |yi| ≤ 109. 
  * After running the given code, the value of tot should be larger than k. 

Examples

Input

4 3


Output

0 0
0 1
1 0
1 1


Input

2 100


Output

no solution
/*
 * To change this template, choose Tools | Templates
 * and open the template in the editor.
 */

import java.io.*;
import java.util.*;

/**
 *
 * @author N-AssassiN
 */
public class Main {

    private static BufferedReader reader;
    private static BufferedWriter out;
    private static StringTokenizer tokenizer;
    //private final static String filename = "filename";

    /**
     * call this method to initialize reader for InputStream and OututStream
     */
    private static void init(InputStream input, OutputStream output) {
        reader = new BufferedReader(new InputStreamReader(input));
        out = new BufferedWriter(new OutputStreamWriter(output));
        //reader = new BufferedReader(new FileReader(filename + ".in"));
        //out = new BufferedWriter(new FileWriter(filename + ".out"));
        tokenizer = new StringTokenizer("");
    }

    /**
     * get next word
     */
    private static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    private static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    private static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    private static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
        init(System.in, System.out);
        int n = nextInt();
        //long startTime = System.currentTimeMillis();
        int k = nextInt();
        int maxTot = (n * (n - 1)) / 2;
        if (maxTot <= k) {
            out.write("no solution\n");
        } else {
            for (int i = 0; i < n; i++) {
                out.write("0 " + i + "\n");
            }
        }
        //long runTime = System.currentTimeMillis() - startTime;
        //out.write(runTime + "\n");
        out.flush();
    }
}