Problem: 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

Solution (in PYTHON):

Solution:
n,m=map(int,raw_input().split())
if m==3:
    if n==3:
        print 0,0
        print 0,1
        print 1,0
    elif n==4:
        print 0,0
        print 0,10
        print 10,0
        print 1,1
    else:
        print -1
    exit(0)
x=10**7
for i in range(m):
    print i,x+i*i
for i in range(n-m):
    print i,-x-i*i