#D4421. Set of Points
Set of Points
Set of Points
Convexity of a set of points on the plane is the size of the largest subset of points that form a convex polygon. Your task is to build a set of n points with the convexity of exactly m. Your set of points should not contain three points that lie on a straight line.
Input
The single line contains two integers n and m (3 ≤ m ≤ 100, m ≤ n ≤ 2m).
Output
If there is no solution, print "-1". Otherwise, print n pairs of integers — the coordinates of points of any set with the convexity of m. The coordinates shouldn't exceed 108 in their absolute value.
Examples
Input
4 3
Output
0 0 3 0 0 3 1 1
Input
6 3
Output
-1
Input
6 6
Output
10 0 -10 0 10 1 9 1 9 -1 0 -2
Input
7 4
Output
176166 6377 709276 539564 654734 174109 910147 434207 790497 366519 606663 21061 859328 886001
inputFormat
Input
The single line contains two integers n and m (3 ≤ m ≤ 100, m ≤ n ≤ 2m).
outputFormat
Output
If there is no solution, print "-1". Otherwise, print n pairs of integers — the coordinates of points of any set with the convexity of m. The coordinates shouldn't exceed 108 in their absolute value.
Examples
Input
4 3
Output
0 0 3 0 0 3 1 1
Input
6 3
Output
-1
Input
6 6
Output
10 0 -10 0 10 1 9 1 9 -1 0 -2
Input
7 4
Output
176166 6377 709276 539564 654734 174109 910147 434207 790497 366519 606663 21061 859328 886001
样例
6 6
0 10000000
1 10000001
2 10000004
3 10000009
4 10000016
5 10000025