CodeForces 312C The Closest Pair（构造）

题意：给你一个程序，要求让你出一组数据，使得这组数据会让程序的tot超过k

思路：很显然我们可以发现，他只是比较了x之间的距离，那么我们可以构造出所有点的x都相同，y都不相同的数据就好了，这样任意两个点的距离一定是大于任意两个点的x坐标之差的

#include<bits\stdc++.h>using namespace std;#define LL long longint main(){LL n,k;scanf("%lld%lld",&n,&k);if(k>=((n*(n-1LL))/2LL))return puts("no solution");for (int i = 0;i<n;i++)printf("1 %d\n",i);}

Description

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 .

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.

Sample Input

Input

4 3

Output

0 00 11 01 1

Input

2 100

Output

no solution