CF1328B K-th Beautiful String

For the given integer $ n $ ( $ n > 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 < t_i $ , and for any $ j $ ( $ 1 \le j < 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): 1. aaabb 2. aabab 3. aabba 4. abaab 5. ababa 6. abbaa 7. baaab 8. baaba 9. babaa 10. 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 > 2 $ ) and $ k $ ( $ 1 \le k \le \frac{n \cdot (n-1)}{2} $ ). Print the $ k $ -th string from the list.

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 $ .

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).