Incremental Double Free Strings

A string is double free if no two adjacent letters are the same.

A string is k-incremental if, for every j from 1 to k, exactly one character occurs j times, and the length of the string is $1+2+3+\cdots+(k-1)+k$. For example, when k = 3, a 3-incremental string has one character that appears once, another that appears twice, and another that appears three times, in any order, for a total length of 6.

A string that meets both conditions is k-incremental and double free. Fix a k and list every such string of lowercase letters in alphabetical order. Here are two examples of that list.

k = 2: aba, aca, ada, ..., aya, aza, bab, bcb, bdb, ..., zxz, zyz

k = 3: ababac, ababad, ..., ababay, ababaz, ababca, ..., zyzyzx

What is the nth string in the alphabetized list of all k-incremental, double free strings?

The input is a single test case. Your program may be run several times on different inputs. The input has exactly one line with two integers k and n ($1 \le k \le 26$, $1 \le n \le 10^{18}$), asking for the nth string in the alphabetically sorted list of all k-incremental, double free strings.

Print the nth k-incremental, double free string in the alphabetized list. If no such string exists, print -1.