Vampires

Felipinho is hooked on his new RPG about wars between vampire clans. In the game he plays a vampire character who keeps fighting vampires from other clans. Each battle is decided by the attributes of the characters involved and by an ordinary six-sided die.

For simplicity, consider only fights between two vampires, vampire 1 and vampire 2. Each has a life energy, called $EV_1$ and $EV_2$ respectively. An attack strength $AT$ and a damage value $D$ are also fixed.

The fight proceeds in turns as follows. Each turn the die is rolled. If the result is less than or equal to $AT$, vampire 1 wins the turn; otherwise vampire 2 wins it. The winner drains $D$ life energy from the opponent: the loser's energy decreases by $D$ and the winner's energy increases by $D$. The fight continues until one of the vampires has an energy less than or equal to zero.

For example, suppose $EV_1=7$, $EV_2=5$, $AT=2$ and $D=4$. The die is rolled and shows 3. Vampire 2 wins the turn, so 4 is subtracted from vampire 1's energy $EV_1$ and added to vampire 2's energy $EV_2$. The new values are $EV_1=3$ and $EV_2=9$. If vampire 2 wins the next turn as well, the fight ends.

$AT$ and $D$ stay constant for the whole fight; only $EV_1$ and $EV_2$ change.

Felipinho loves the game, but he finds the fights far too long, and he would like to know his chance of winning in advance so he can decide whether a fight is worth it. Write a program that, given the initial values of $EV_1$ and $EV_2$ together with $AT$ and $D$, computes the probability that vampire 1 wins the fight.

The input contains several test cases. Each test case is a single line with four integers $EV_1$, $EV_2$, $AT$ and $D$ separated by spaces ($1 \le EV_1, EV_2 \le 10$, $1 \le AT \le 5$, $1 \le D \le 10$).

The end of the input is marked by a line containing four zeros separated by spaces. Do not process this line.

For each test case, print a single line with one real number: the probability that vampire 1 wins the fight, expressed as a percentage, with exactly one digit after the decimal point.

Round the exact probability to one decimal place. When the exact value lies exactly halfway (for example, exactly $56.25$), round up and print $56.3$.