算法练习：URAL 1495 One-two, One-two 2

Description
A year ago the famous gangster Vito Maretti woke up in the morning and realized that he was bored of robbing banks of round sums. And for the last year he has been taking from banks sums that have only digits 1 and 2 in their decimal notation. After each robbery, Vito divides the money between N members of his gang. Your task is to determine the minimal stolen sum which is a multiple of N.

Input

The input contains the number N (1 ≤  N ≤ 10 6).

Output
Output the minimal number which is a multiple of N and whose decimal notation contains only digits 1 and 2. If it contains more than 30 digits or if there are no such numbers, then output "Impossible".

Sample Input

input                output
5                        Impossible

8                        112

解析：令y = x * 10 + i，其中i等于1或2，这样可以逐一求出余数，若余数为零，则返回由1和2组成的字符串。不过因为数据会很大，为避免超时，要利用取模公式做一些化简。

           y%n = (10x + i)%n

                   = ((10x)%n + i%n)%n

                   = ((10%n * x%n)%n + i%n)%n

                   = ((10%n * x.mod)%n + i%n)%n      // ((a*b) mod p*c) mod p = (a*(b*c) mod p) mod p

                   = (((1 * 10)%n * x.mod)%n + i%n)%n

                   = ((1 * (10 * x.mod)%n)%n + i%n)%n    //(a mod p) mod p = a mod p

                   = ((10 * x.mod)%n + i%n)%n

                   = (10 * x.mod + i)%n

           则y.mod = (10 * x.mod + i)%n                

           另外，当遇到余数一样时，则不用考虑后出现的数，因为相同的余数中，先出现的倍数比较小。

           代码参考：http://blog.youkuaiyun.com/kewowlo/article/details/43346497