## Baltic OI '08 P3 - Magical Stones

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Points: 20 (partial)
Time limit: 1.0s
Memory limit: 32M

Problem type
##### Baltic Olympiad in Informatics: 2008 Day 1, Problem 3

Famous stones Xi-- can only be found in Wonderland. Such a stone is simply a granite board with an inscription consisting only of letters X and I. Each board contains exactly letters. There are not more than positions in each board where letters X and I are next to each other. The top and bottom sides of the stones are not fixed, so the stones can be rotated upside-down. For instance two figures below depict exactly the same stone:

IXXIIXXX       XXXIIXXI
Two ways of looking at the same stone. This stone is of type Xi--, but also Xi-- (and also of any type Xi-- for ).

No two magic stones in Wonderland are the same, i.e. no two stones contain the same inscription (re?member that the upside-down rotation of a stone is allowed). If it is possible to read the inscription of some stone in two different ways (using the upside-down rotation) then the canonical representation of the stone is defined as the lexicographically less of these two ways of reading the inscription. If a stone's inscription is symmetrical, i.e. the upside-down rotation does not change it, then its canonical representation is defined as the unique way of reading this inscription.

Example: There are exactly stones of type Xi--. Their canonical representations written in lexicographical order are: III, IIX, IXI, IXX, XIX and XXX.

Alice is a well-known expert on the Xi-- stones from Wonderland. She would like to create a lexicographical index of the canonical representations of all stones of type Xi-- (for some specific values of and ).

What inscription should be written at position of the index, for a given value of ?

#### Input Specification

The first and only line contains three space-seperated integers , and .

#### Output Specification

The only line of output should contain the (in the lexicographical order) canonical representation of a Xi-- stone. If the number of Xi-- stones is less than , then output NO SUCH STONE.

#### Sample Input 1

3 2 5

#### Sample Output 1

XIX

#### Sample Input 2

3 2 7

#### Sample Output 2

NO SUCH STONE