Killjee has got a matrix and now he is trying represent it in a ZIg-Zag format.  

The zigzag format of a matrix is representation of its diagonals in separate line.

Where,  $I_{th}$ line of output contains $i_{th}$ top right - bottom left diagonal if I is odd.

$I_{th}$ line of output should contain $I_{th}$ bottom left - top right diagonal.  If I is even.

See sample explanation for better understanding.

INPUT

First line of input contain two space separated integers $N$ and $M$, where $N$ is number of rows in matrix and $M$ is number of columns in matrix.

OUTPUT

Output Zig-Zag representation of given matrix;

CONSTRAINTS

$1 \le n,m \le 1000$

$1 \le a_i \le 10^9$