A string is called double free if no
two adjacent letters are the same.
A string is called $k$incremental if for all values
of $j$ in the range
$[1,k]$, there exists
exactly one character with $j$ occurrences, and the string’s
length is $1+2+3+\ldots
+(k1)+k$. For example, if $k=3$, then a $3$incremental string should have
one character appear once, another twice, another three times,
in any order, for a total string length of $6$.
A string is both $k$incremental and double free if it meets both these criteria. Now
consider examining all such strings of lowercase letters for a
given $k$ in alphabetical
order. Consider the following examples.
$k=2$: aba, aca, ada, …, aya, aza, bab, bcb, bdb, …, zxz, zyz
$k=3$: ababac, ababad, …,
ababay, ababaz,
ababca, …, zyzyzx
What is the $n^\mathrm
{th}$ string in an alphabetized list of all $k$incremental, double free strings?
Input
Each input will consist of a single test case. Note that
your program may be run multiple times on different inputs.
There will be exactly one line of input. It will contain two
integers, $k$ and
$n$ ($1 \le k \le 26, 1 \le n \le
10^{18}$), which is asking for the $n^\mathrm {th}$ string in the
alphabetically sorted list of all $k$incremental, double free strings.
Output
Output the $n^\mathrm
{th}$ $k$incremental, double free string in the alphabetized list. If
no such string exists, output $1$.
Sample Input 1 
Sample Output 1 
2 650

zyz

Sample Input 2 
Sample Output 2 
2 651

1

Sample Input 3 
Sample Output 3 
5 12345678901234

yuzczuyuyuzuyci
