Magic Stone

Archaeologist Seonyeong found a mysterious magic stone in an unknown world. A string made only of the characters I and X is engraved on the stone.

For given n and k, an n-k magic stone is a stone whose string has length n and has at most k adjacent pairs whose two characters are different. In other words, count the positions j where the j-th and (j+1)-st characters are one I and one X; this count must be at most k.

Rotating a stone by 180 degrees reverses the string, and the rotated stone is considered the same stone. Therefore, for each pair of a string and its reverse, only the lexicographically smaller string is considered. The character I comes before X.

After all n-k magic stones are sorted in lexicographic order, find the i-th stone.

The first line contains n, k, and i (0 <= k < n <= 60, 0 < i < 10^18).

If the i-th n-k magic stone exists, print it. Otherwise, print NO SUCH STONE.

The 3-2 magic stones are III, IIX, IXI, IXX, XIX, and XXX, for a total of 6 stones.