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 < in modern programming languages.

For example, if $$$n=5$$$ the strings are (the order does matter):

aaabb
aabab
aabba
abaab
ababa
abbaa
baaab
baaba
babaa
bbaaa

It is easy to show that such a list of strings will contain exactly $$$\frac{n \cdot (n-1)}{2}$$$ strings.

You are given $$$n$$$ ($$$n \gt 2$$$) and $$$k$$$ ($$$1 \le k \le \frac{n \cdot (n-1)}{2}$$$). Print the $$$k$$$-th string from the list.

Input

The input contains one or more test cases.

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 $$$k$$$ ($$$3 \le n \le 10^5, 1 \le k \le \min(2\cdot10^9, \frac{n \cdot (n-1)}{2})$$$.

The sum of values $$$n$$$ over all test cases in the test doesn't exceed $$$10^5$$$.

Output

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).

K-th Beautiful String

Examples