Online Judge | Problem Set | Authors | Online Contests | User | ||||||
---|---|---|---|---|---|---|---|---|---|---|

Web Board Home Page F.A.Qs Statistical Charts | Current Contest Past Contests Scheduled Contests Award Contest |

Language: Alternative Scale of Notation
Description One may define a map of strings over an alphabet Σ _{B} = { C1, C2, . . . C_{B} } of size B to non-negative integer numbers, using characters as digits C1 = 0, C2 = 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 α[ 1...n ] of length n we put
_{B}(α)=Σ_{0<=i<=n-1}α[n-i]*B^{i}For example, U3(1001) = 1*27 + 0*9 + 0*3 + 1*1 = 28. However, this correspondence has one major drawback: it is not ont-to-one. For example, 28 = U3(1001) = U3(01001) = U3(001001) = ... , infinitely many strings map to the number 28. 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: C1 = 1, C2 = 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 α[ 1...n ] of length n we put
_{B}(α)=Σ_{0<=i<=n-1}α[n-i]*B^{i}For an empty string ε we put V _{B}(ε) = 0.
This map looks very much like U _{B} , however, the set of digits is now different. So, for example, we have V3(1313) = 1*27 + 3*9 + 1*3 + 3*1 = 60.
It can be easily proved that the correspondence defined by this map is one-to-one 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 α, such that V_{B}(α) = x.
Input 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 Output in one line such string α, consisting only of digits from the set { 1, 2, . . . , B }, that V _{B}(α) = x .
Sample Input 3 60 Sample Output 1313 Source |

[Submit] [Go Back] [Status] [Discuss]

All Rights Reserved 2003-2013 Ying Fuchen,Xu Pengcheng,Xie Di

Any problem, Please Contact Administrator