CF1761A Two Permutations

You are given three integers $ n $ , $ a $ , and $ b $ . Determine if there exist two permutations $ p $ and $ q $ of length $ n $ , for which the following conditions hold: - The length of the longest common prefix of $ p $ and $ q $ is $ a $ . - The length of the longest common suffix of $ p $ and $ q $ is $ b $ . A permutation of length $ n $ is an array containing each integer from $ 1 $ to $ n $ exactly once. For example, $ [2,3,1,5,4] $ is a permutation, but $ [1,2,2] $ is not a permutation ( $ 2 $ appears twice in the array), and $ [1,3,4] $ is also not a permutation ( $ n=3 $ but there is $ 4 $ in the array).

Each test contains multiple test cases. The first line contains a single integer $ t $ ( $ 1\leq t\leq 10^4 $ ) — the number of test cases. The description of test cases follows. The only line of each test case contains three integers $ n $ , $ a $ , and $ b $ ( $ 1\leq a,b\leq n\leq 100 $ ).

For each test case, if such a pair of permutations exists, output "Yes"; otherwise, output "No". You can output each letter in any case (upper or lower).

In the first test case, $ [1] $ and $ [1] $ form a valid pair. In the second test case and the third case, we can show that such a pair of permutations doesn't exist. In the fourth test case, $ [1,2,3,4] $ and $ [1,3,2,4] $ form a valid pair.