
ZOJ Problem Set  2461
One may define a map of strings over an alphabet = { C_{1}, C_{2}, . . . C_{B} } of size B to nonnegative integer numbers, using characters as digits C_{1} = 0, C_{2} = 1, . . . , C_{B} = B  1 and interpreting the string as the representation of some number in a scale of notation with base B. Let us denote this map by U_{B} , for a string [ 1...n ] of length n we put For example, U_{3}(1001) = 1*27 + 0*9 + 0*3 + 1*1 = 28. However, this correspondence has one major drawback: it is not onttoone. For example, In mathematical logic and computer science this may be unacceptable. To overcome this problem, the alternative interpretation is used. Let us interpret characters as digits, but in a slightly different way: C_{1} = 1, C_{2} = 2, . . . , C_{B} = B . Note that now we do not have 0 digit, but rather we have a rudiment B digit. Now we define the map V_{B} in a similar way, for each string [ 1...n ] of length n we put For an empty string we put V_{B}( ) = 0. This map looks very much like U_{B} , however, the set of digits is now different. So, for example, we have V_{3}(1313) = 1*27 + 3*9 + 1*3 + 3*1 = 60. It can be easily proved that the correspondence defined by this map is onetoone and onto. Such a map is called bijective, and it is well known that every bijective map has an inverse. Your task in this problem is to compute the inverse for the map V_{B} . That is, for a given integer number x you have to find the string , such that V_{B}( ) = x. Input SpecificationInput consists of several test cases. For each case, the first line contains B (2 <= B <= 9) and the second line contains an integer number x given in a usual decimal scale of notation, 0 <= x <= 10^{100}. Output SpecificationFor each test case, output in one line such string , consisting only of digits from the set { 1, 2, . . . , B }, that V_{B}( ) = x . Sample Input3 60 3 0 2 31 Output for the Sample Input1313 11111 Source: Northeastern Europe 2003 