Baltic Olympiad in Informatics: 2008 Day 1, Problem 3

Famous stones Xi-~n~-~k~ 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 ~n~ letters. There are not more than ~k~ 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-~8~-~3~, but also Xi-~8~-~4~ (and also of any type Xi-~8~-~k~ for ~k \ge 3~).

No two magic stones in Wonderland are the same, i.e. no two stones contain the same inscription (remember 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 ~6~ stones of type Xi-~3~-~2~. Their canonical representations written in lexicographical order are: III, IIX, IXI, IXX, XIX and XXX.

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

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

Constraints

~0 \le k < n \le 60~

~0 < i < 10^{18}~

Input Specification

The first and only line contains three space-separated integers ~n~, ~k~ and ~i~.

Output Specification

The only line of output should contain the ~i^\text{th}~ (in the lexicographical order) canonical representation of a Xi-~n~-~k~ stone.

If the number of Xi-~n~-~k~ stones is less than ~i~, 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