Given two positive integers m and n, print an m x n matrix containing the numbers from 1 to m * n. Odd rows go left to right, even rows go right to left.

Input

• One line containing two positive integers m and n.

Output

• Numbers on the same line are separated by exactly one space.

Constraints

• 1 <= m, n <= 50

Example

Input

4 5

Output

1 2 3 4 5
10 9 8 7 6
11 12 13 14 15
20 19 18 17 16