Lucky Probability

题意翻译

Petya 喜欢幸运数字（整数），幸运数字必须是只包含 $4$ 和 $7$ 两个整数。一天，Petya 和她的 Vasya 朋友玩游戏，Petya 会在闭区间 $[pl,pr]$ 中等概率地选出一个整数 $p$ ，Vasya 则在闭区间 $[vl,vr]$ 中等概率地选出一个整数 $v$。如果 $v>p$ 则交换 $v$ 和 $p$。求满足闭区间 $[v,p]$ 恰好包含 $k$ 个幸运数的概率是多少？答案的绝对误差不超过 $10^{-9}$。

题目描述

Petya loves lucky numbers. We all know that lucky numbers are the positive integers whose decimal representations contain only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not. Petya and his friend Vasya play an interesting game. Petya randomly chooses an integer $ p $ from the interval $ [p_{l},p_{r}] $ and Vasya chooses an integer $ v $ from the interval $ [v_{l},v_{r}] $ (also randomly). Both players choose their integers equiprobably. Find the probability that the interval $ [min(v,p),max(v,p)] $ contains exactly $ k $ lucky numbers.

输入输出格式

输入格式

The single line contains five integers $ p_{l} $ , $ p_{r} $ , $ v_{l} $ , $ v_{r} $ and $ k $ ( $ 1<=p_{l}<=p_{r}<=10^{9},1<=v_{l}<=v_{r}<=10^{9},1<=k<=1000 $ ).

输出格式

On the single line print the result with an absolute error of no more than $ 10^{-9} $ .

输入输出样例

输入样例 #1

1 10 1 10 2

输出样例 #1

0.320000000000

输入样例 #2

5 6 8 10 1

输出样例 #2

1.000000000000

说明

Consider that $ [a,b] $ denotes an interval of integers; this interval includes the boundaries. That is,  In first case there are $ 32 $ suitable pairs: $ (1,7),(1,8),(1,9),(1,10),(2,7),(2,8),(2,9),(2,10),(3,7),(3,8),(3,9),(3,10),(4,7),(4,8),(4,9),(4,10),(7,1),(7,2),(7,3),(7,4),(8,1),(8,2),(8,3),(8,4),(9,1),(9,2),(9,3),(9,4),(10,1),(10,2),(10,3),(10,4) $ . Total number of possible pairs is $ 10·10=100 $ , so answer is $ 32/100 $ . In second case Petya always get number less than Vasya and the only lucky $ 7 $ is between this numbers, so there will be always $ 1 $ lucky number.

题意翻译

Petya 喜欢幸运数字（整数），幸运数字必须是只包含 $4$ 和 $7$ 两个整数。一天，Petya 和她的 Vasya 朋友玩游戏，Petya 会在闭区间 $[pl,pr]$ 中等概率地选出一个整数 $p$ ，Vasya 则在闭区间 $[vl,vr]$ 中等概率地选出一个整数 $v$。如果 $v>p$ 则交换 $v$ 和 $p$。求满足闭区间 $[v,p]$ 恰好包含 $k$ 个幸运数的概率是多少？答案的绝对误差不超过 $10^{-9}$。