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 PYTHON3):

Solution:
def f(x):
    return int(x * x + 1e7)
    
def g(x):
    return -f(x)
    
n, m = map(int, input().split())

if(m == 3):
    if(n == 3):
        print('0 0')
        print('1 0')
        print('0 1')
    elif(n == 4):
        print('0 0')
        print('1 1')
        print('10000 0')
        print('0 10000')
    else:
        print(-1)
else:
    for i in range(m):
        print(i, f(i))
    for i in range(n - m):
        print(i, g(i))