The task is to find the $k$-th (in lexicographical order) non-empty word consisting of at most $n$ letters from the set $\{a, b, c\}$ such that any two adjacent letters in the word are different.

Recall that a word $s$ is smaller than a word $t$ ($s \neq t$) in lexicographical order if $s$ is a prefix of $t$ or if at the first position where $s$ and $t$ differ, the letter in $s$ is smaller (in alphabetical order) than the letter in $t$.

Input

The only line of input contains two integers $n$ and $k$ ($1 \le n \le 10^6$, $1 \le k \le 10^{18}$) as described in the problem.

Output

If there are fewer than $k$ words satisfying the problem conditions, output NIE. Otherwise, the only line of output should contain the requested word.

Examples

Input 1

3 7

Output 1

acb

Input 2

2 10

Output 2

NIE