Rectangle Division

Anya is playing a new board game, "Checkered Kingdom".

Consider a rectangular grid board of size $a \times b$.

The board must be divided into $m$ rectangles using vertical or horizontal cuts. The rectangles do not have to be equal in size. Exactly $k$ cuts must be made in total.

Each cut is a straight line from one edge of the board to the opposite edge. Cuts can only be made along grid lines, the borders between cells.

Print how many horizontal cuts ($0 \le h < a$) and how many vertical cuts ($0 \le v < b$) are made. If the board can be cut in several ways, print the one with fewer horizontal cuts. If the board cannot be cut as required, print -1.

The first line contains a single integer $t$, the number of tests ($1 \le t \le 100$). Each of the next $t$ lines contains four integers separated by spaces: $a$, $b$, $k$, $m$, the height and width of the board, the number of cuts, and the number of rectangles ($1 \le a, b \le 10^9$, $0 \le k \le 2 \cdot 10^9$, $1 \le m \le 10^{18}$, $k < m$).

For each test, print two integers $h$ and $v$ separated by a space: the number of horizontal cuts and the number of vertical cuts, if the board can be cut as required. Otherwise, print -1.

The example has three tests.

1. In the first test, the board can be cut as shown in the figure:

Illustration for the first test: $a = 2$, $b = 2$, $k = 1$, $m = 2$.

2. In the second test, the board cannot be cut as required.

3. In the third test, the board can be cut as shown in the figure:

Illustration for the third test: $a = 3$, $b = 5$, $k = 5$, $m = 12$.