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B. Set of Points

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputConvexity 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* ≤ 2*m*).

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 10^{8} 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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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