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