Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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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

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