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.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;

public class CF {

	public static void main(String[] args) {
		FasterScanner sc = new FasterScanner();
		int N =sc.nextInt();
		int K  =sc.nextInt();
		if(((N*(N-1))>>1)<=K){
			System.out.println("no solution");
			return;
		}
		for(int a=0;a<N;a++){
			System.out.println(a+" "+(a*200000));
		}
		
	}
	static class FasterScanner{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		
		public FasterScanner(){
			stream = System.in;
			//stream = new FileInputStream(new File("dec.in"));

		}
		int read(){
			if(numChars==-1)
				throw new InputMismatchException();
			if(curChar>=numChars){
				curChar = 0;
				try{
					numChars = stream.read(buf);
				} catch (IOException e){
					throw new InputMismatchException();
				}
				if(numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		
		boolean isSpaceChar(int c){
			return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
		}
		boolean isEndline(int c){
			return c=='\n'||c=='\r'||c==-1;
		}
		int nextInt(){
			return Integer.parseInt(next());
		}
		long nextLong(){
			return Long.parseLong(next());
		}
		double nextDouble(){
			return Double.parseDouble(next());
		}
		String next(){
			int c = read();
			while(isSpaceChar(c))
				c=read();
			StringBuilder res = new StringBuilder();
			do{
				res.appendCodePoint(c);
				c=read();
			} while(!isSpaceChar(c));
			return res.toString();
		}
		String nextLine(){
			int c = read();
			while(isEndline(c))
				c=read();
			StringBuilder res = new StringBuilder();
			do{
				res.appendCodePoint(c);
				c = read();
			}while(!isEndline(c));
			return res.toString();
		}
		
	}

}
