The Vanishing
In games like DD (Dungeons and Dragons), the outcome of a move is determined using dice with various numbers of sides. Each side of a die is numbered from 1 to N, where N represents the number of sides. The damage inflicted by a weapon is calculated using the formula (M dN + K), where M dN signifies the total from rolling an N-sided die M times, and K is a fixed natural number. For instance, 3 d6 + 4 means rolling a standard 6-sided die 3 times, summing the results, and adding 4 to the total.
In this game, you face a clever monster called the Boojum. The Boojum has a unique trait: it will be defeated if it receives exactly Q units of damage, where Q is a natural number.
If the damage dealt is anything other than Q, the Boojum will survive and, on its turn, make you vanish. Fortunately, you get to act before the Boojum does.
Given the values M, N, K, and Q, calculate the probability of destroying the Boojum with this weapon.
Input
The weapon's parameters are given in the form M dN+K, followed by the required damage Q on the next line. The numbers M and N are natural numbers and do not exceed 30. The numbers K and Q are natural numbers and do not exceed 1000.
Output
Output the probability that the damage dealt will exactly equal Q, expressed as a percentage with two decimal places.