A. Two Permutations
brute force; constructive algorithms
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.