CF1202D Print a 1337-string...

The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. You are given an integer $ n $ . You have to find a sequence $ s $ consisting of digits $ \{1, 3, 7\} $ such that it has exactly $ n $ subsequences equal to $ 1337 $ . For example, sequence $ 337133377 $ has $ 6 $ subsequences equal to $ 1337 $ : 1. $ 337\underline{1}3\underline{3}\underline{3}7\underline{7} $ (you can remove the second and fifth characters); 2. $ 337\underline{1}\underline{3}3\underline{3}7\underline{7} $ (you can remove the third and fifth characters); 3. $ 337\underline{1}\underline{3}\underline{3}37\underline{7} $ (you can remove the fourth and fifth characters); 4. $ 337\underline{1}3\underline{3}\underline{3}\underline{7}7 $ (you can remove the second and sixth characters); 5. $ 337\underline{1}\underline{3}3\underline{3}\underline{7}7 $ (you can remove the third and sixth characters); 6. $ 337\underline{1}\underline{3}\underline{3}3\underline{7}7 $ (you can remove the fourth and sixth characters). Note that the length of the sequence $ s $ must not exceed $ 10^5 $ . You have to answer $ t $ independent queries.

The first line contains one integer $ t $ ( $ 1 \le t \le 10 $ ) — the number of queries. Next $ t $ lines contains a description of queries: the $ i $ -th line contains one integer $ n_i $ ( $ 1 \le n_i \le 10^9 $ ).

For the $ i $ -th query print one string $ s_i $ ( $ 1 \le |s_i| \le 10^5 $ ) consisting of digits $ \{1, 3, 7\} $ . String $ s_i $ must have exactly $ n_i $ subsequences $ 1337 $ . If there are multiple such strings, print any of them.