Two Permutations

1000ms

262144K

Description:

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).

Input:

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 $$$b$$$ ($$$1\leq a,b\leq n\leq 100$$$).

Output:

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).

Sample Input:

Sample Output:

Yes
No
No
Yes

Note:

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.

Informação

Provedor Codeforces

Código CF1761A