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ZOJ Problem Set - 2461
Alternative Scale of Notation

Time Limit: 2 Seconds      Memory Limit: 65536 KB

One may define a map of strings over an alphabet = { C1, C2, . . . CB } of size B to non-negative integer numbers, using characters as digits C1 = 0, C2 = 1, . . . , CB = 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 UB , for a string [ 1...n ] of length n we put

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, . . . , CB = B . Note that now we do not have 0 digit, but rather we have a rudiment B digit. Now we define the map VB in a similar way, for each string [ 1...n ] of length n we put

For an empty string we put VB( ) = 0.

This map looks very much like UB , 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 VB . That is, for a given integer number x you have to find the string , such that VB( ) = x.

### Input Specification

Input 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 <= 10100.

### Output Specification

For each test case, output in one line such string , consisting only of digits from the set { 1, 2, . . . , B }, that VB( ) = x .

```3
60
3
0
2
31
```

### Output for the Sample Input

```1313

11111
```

Source: Northeastern Europe 2003
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