ABC

Given integers $N$ and $K$, write a program that finds a string $S$ meeting both of these conditions.

• $S$ has length $N$ and uses only the characters A, B, and C.
• Exactly $K$ pairs $(i, j)$ satisfy $0 \le i < j < N$ and S[i] < S[j].

Characters compare in alphabetical order, so A < B < C.

The first line contains $N$ and $K$, separated by a space. ($3 \le N \le 30$, $0 \le K \le N(N-1)/2$)

Print on the first line the lexicographically smallest string $S$ that meets the conditions. If no such $S$ exists, print -1.