CF1451B Non-Substring Subsequence

Hr0d1y has $ q $ queries on a binary string $ s $ of length $ n $ . A binary string is a string containing only characters '0' and '1'. A query is described by a pair of integers $ l_i $ , $ r_i $ $ (1 \leq l_i \lt r_i \leq n) $ . For each query, he has to determine whether there exists a good subsequence in $ s $ that is equal to the substring $ s[l_i\ldots r_i] $ . - A substring $ s[i\ldots j] $ of a string $ s $ is the string formed by characters $ s_i s_{i+1} \ldots s_j $ . - String $ a $ is said to be a subsequence of string $ b $ if $ a $ can be obtained from $ b $ by deleting some characters without changing the order of the remaining characters. - A subsequence is said to be good if it is not contiguous and has length $ \ge 2 $ . For example, if $ s $ is "1100110", then the subsequences $ s_1s_2s_4 $ ("1100110") and $ s_1s_5s_7 $ ("1100110") are good, while $ s_1s_2s_3 $ ("1100110") is not good. Can you help Hr0d1y answer each query?

The first line of the input contains a single integer $ t $ ( $ 1\leq t \leq 100 $ ) — the number of test cases. The description of each test case is as follows. The first line contains two integers $ n $ ( $ 2 \leq n \leq 100 $ ) and $ q $ ( $ 1\leq q \leq 100 $ ) — the length of the string and the number of queries. The second line contains the string $ s $ . The $ i $ -th of the next $ q $ lines contains two integers $ l_i $ and $ r_i $ ( $ 1 \leq l_i \lt r_i \leq n $ ).

For each test case, output $ q $ lines. The $ i $ -th line of the output of each test case should contain "YES" if there exists a good subsequence equal to the substring $ s[l_i...r_i] $ , and "NO" otherwise. You may print each letter in any case (upper or lower).

In the first test case, - $ s[2\ldots 4] = $ "010". In this case $ s_1s_3s_5 $ ("001000") and $ s_2s_3s_6 $ ("001000") are good suitable subsequences, while $ s_2s_3s_4 $ ("001000") is not good. - $ s[1\ldots 3] = $ "001". No suitable good subsequence exists. - $ s[3\ldots 5] = $ "100". Here $ s_3s_5s_6 $ ("001000") is a suitable good subsequence.