Zigzag Number Grid

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given $n$ rows and $m$ columns, use 1-based row numbers. Odd rows contain $1,2,\ldots,m$; even rows contain $m,m-1,\ldots,1$. Print exactly $n$ rows and $m$ integers per row, separated by one space and without trailing spaces.

Input

One line contains integers $n,m$, the row and column counts.

Output

Print exactly $n$ rows.

Subtasks

• Subtask 1 (20%): $1\le n,m\le 3$.

• Subtask 2 (30%): $1\le n,m\le 8$.

• Subtask 3 (50%): $1\le n,m\le 15$.

Examples

Example 1

Input:

3 4

Output:

1 2 3 4
4 3 2 1
1 2 3 4

Explanation:

Odd rows increase; even rows decrease.

Example 2

Input:

1 1

Output:

1

Explanation:

Odd rows increase; even rows decrease.