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
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main
{
  static BufferedReader reader;
  static StringTokenizer tokenizer;
  static PrintWriter writer;
  
  static int nextInt() throws IOException
  {
    return Integer.parseInt(nextToken());
  }
  
  static long nextLong() throws IOException
  {
    return Long.parseLong(nextToken());
  }
  
  static double nextDouble() throws IOException
  {
    return Double.parseDouble(nextToken());
  }
  
  static boolean eof = false;
  
  static String nextToken() throws IOException
  {
    while (tokenizer == null || !tokenizer.hasMoreTokens())
    {
      tokenizer = new StringTokenizer(reader.readLine());
    }
    return tokenizer.nextToken();
  }
  
  public static void main(String[] args) throws IOException
  {
    tokenizer = null;
    reader = new BufferedReader(new InputStreamReader(System.in));
    writer = new PrintWriter(System.out);
    banana();
    reader.close();
    writer.close();
  }
  
  static int test(int a[], int b[])
  {
    int sum = 0;
    for (int i = 0; i < a.length; ++i)
      sum += a[i] * b[i];
    
    return sum;
  }
  
  static void banana() throws IOException
  {
    int n = nextInt();
    int k = nextInt();
    
    if (k >= n * (n - 1) / 2)
      System.out.println("no solution");
    else
    {
      for (int i = 0; i < n; ++i)
      {
        System.out.println(i + " " +i * 2 * n) ;
      }
    }
  }
}