(p, q) - horse
(p, q)-horse - a generalization of the usual chess knight. (p, q)-horse moves under its own power on p cells in the same direction, and q - in the other (perpendicular). For example, (3, 4)-the horse can move with the cells (5, 6) cells (1, 3), (2, 2), (2, 10), (1, 9), (8, 10), (9, 9), (8, 2) and (9, 3). Obviously, the usual chess knight - a (2, 1)-horse.
Your task - to determine the minimum number of moves it takes (p, q)-horse to get from one cell checkerboard M×N to the other. Go beyond the board is prohibited.
Input
One line contains 8 integers M, N, p, q, x_1, y_1, x_2, y_2 (1 ≤ x_1, x_2 ≤ M ≤ 100, 1 ≤ y_1, y_2 ≤ N ≤ 100, 0 ≤ p ≤ 100, 0 ≤ q ≤ 100).
Output
The first line print the number of moves k it takes (p, q)-horse to get out of the cell (x_1, y_1) to the cell (x_2, y_2). Next to follow k+1 rows with the provisions of (p, q)-horse in this way.
If (p, q)-horse can not get from (x_1, y_1) to (x_2, y_2), output -1.