Dragon Milkdrinker

Hard times have come upon the citizens of Bytevillage. A dragon known as the Milkdrinker has appeared near their village. It has declared that on the first day of every month it will come to the village and demand a tribute of $h$ milliliters of milk. If it does not receive the tribute, it will burn the village to ashes.

Prince Byteman is deeply worried about the dragon's threat. He wonders what the probability is that the demand cannot be met. He knows there are $n$ cows in the village, and that each cow's monthly milk yield (in milliliters) is a real number chosen uniformly at random from the interval $[m, M]$, independently of the other cows.

Help Prince Byteman compute the probability of the unfortunate situation in which the total amount of milk produced by the cows falls short of the demand $h$ and the village is burned. In other words, compute the probability that the sum of the $n$ cows' yields is strictly less than $h$.

The first line of standard input contains five integers $n$, $m$, $M$, $h$, and $d$ ($1 \le n \le 3000$, $0 \le m \le M \le 10^9$, $0 \le h \le 10^9$, $1 \le d \le 10000$). They denote, respectively: the number of cows in the village, the minimum monthly yield, the maximum monthly yield, the size of the tribute, and the required number of digits after the decimal point in the output.

Print a single line containing the probability $p$, an approximation of the chance that the dragon's demand is not met, written as a decimal fraction. The value must be rounded down (truncated) to exactly $d$ digits after the decimal point.