For the given integer $n$ $(n\gt 2)$ let's write down all the strings of length $n$ which contain $n−2$ letters `a` and two letters `b` in lexicographical (alphabetical) order. Recall that the string $s$ of length $n$ is lexicographically less than string $t$ of length $n$, if there exists such $i$ $(1\le i\le n)$, that $s_i\lt t_i$, and for any $j$ $(1\le j\lt i)$ $s_j=t_j$. The lexicographic comparison of strings is implemented by the operator $\lt$ in modern programming languages. For example, if $n=5$ the strings are (the order does matter): 1. $\text{aaabb}$ 2. $\text{aabab}$ 3. $\text{aabba}$ 4. $\text{abaab}$ 5. $\text{ababa}$ 6. $\text{abbaa}$ 7. $\text{baaab}$ 8. $\text{baaba}$ 9. $\text{babaa}$ 10. $\text{bbaaa}$ It is easy to show that such a list of strings will contain exactly $\large\frac{n\cdot (n−1)}{2}$ strings. You are given $n$ $(n\gt 2)$ and $k$ $(1\le k\le {\large\frac{n\cdot (n−1)}{2}})$. Print the $k$-th string from the list.

The first line contains one integer $t$ $(1\le t\le 10^4)$ — the number of test cases in the test. Then $t$ test cases follow. Each test case is written on the the separate line containing two integers $n$ and $k$ $(3\le n\le 10^5,1\le k\le\min(2\cdot 10^9,{\large\frac{n\cdot (n−1)}{2}}))$. The sum of values $n$ over all test cases in the test doesn't exceed $10^5$.

For each test case print the $k$-th string from the list of all described above strings of length $n$. Strings in the list are sorted lexicographically (alphabetically).

Codeforces Div. 3 [CF1328B]