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A. The Closest Pair
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 (x 1, y 1) and (x 2, y 2) is .

The pseudo code of the unexpected code is as follows:

input nfor 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 secondd=INF        //here INF is a number big enoughtot=0for 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 x i, y i (|x i|, |y i| ≤ 109) representing the coordinates of the i-th point.

The conditions below must be held:

• All the points must be distinct.
• |x i|, |y i| ≤ 109.
• After running the given code, the value of tot should be larger than k.
Examples
Input
4 3
Output
0 00 11 01 1
Input
2 100
Output
no solution