Rain Fall

Rainfall is measured in millimeters. Rain is collected in a vertical, transparent tube marked with millimeter graduations, so once the rain stops you can read off the height of the water inside the tube.

Unfortunately the tube has a leak at height $L$ mm. Whenever the water level is above the leak, water drains out of the tube at a rate of $K$ millimeters per hour (mm/h).

We want to determine how much rain actually fell during one particular rainfall. Assume the tube is tall enough that it never overflows, that rain falls at an (unknown) constant rate for the whole duration of the rainfall, and that no water evaporates. The height (thickness) of the leak itself is negligible.

The input is a single line with five positive numbers $L$ $K$ $T_1$ $T_2$ $H$:

• $L$ — the height of the leak (mm)
• $K$ — the rate at which water drains through the leak (mm/h)
• $T_1$ — the duration of the rainfall (h)
• $T_2$ — the time between the end of the rainfall and the observation of the water level (h)
• $H$ — the observed water level in the tube (mm)

Every number is between $0.01$ and $1000.00$ inclusive and is given with exactly two decimals.

Print one line with two numbers $F_1$ and $F_2$, separated by a single space and each rounded to exactly six decimal places. $F_1$ is the smallest total rainfall (in mm) that is consistent with the observation, and $F_2$ is the largest.