The lame king moves on a grid board of size $n \times m$, each time moving from the current cell to a side-adjacent neighboring cell. We denote the cell in row $x$ and column $y$ as $(x, y)$.

The lame king must visit all cells, visiting each cell exactly once, and return to the starting cell. At the same time, two neighboring cells $(x_1, y_1)$ and $(x_2, y_2)$ are marked on the board. In the king’s traversal of the board, the cells $(x_1, y_1)$ and $(x_2, y_2)$ must appear consecutively: after being in one of them, he must immediately move to the other.

Output a suitable order of traversal of the board, or determine that it does not exist.

Input Format

The first line contains two integers $n$ and $m$ $(2 \le n, m \le 1000)$ — the board dimensions.
The second line contains four integers $x_1, y_1, x_2, y_2$ — the coordinates of two neighboring cells $(1 \le x_1, x_2 \le n;\ 1 \le y_1, y_2 \le m;\ |x_1 - x_2| + |y_1 - y_2| = 1)$.

Output Format

If such a traversal does not exist, output a single number $-1$.
Otherwise, output $n \times m + 1$ pairs of numbers — the coordinates of the cells in the order of traversal; the starting cell must be printed twice, at the beginning and at the end.

Scoring

There are 50 tests in this problem, each scored independently with 2 points.
During the contest, you are informed of the checking result on each test.

Example

Standard Input

4 3
2 2 3 2

Standard Output

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

Standard Input

3 5
1 2 2 2

Standard Output

-1

Note

The figure shows a traversal of the board for the first example.