Description: Let's call an integer array $$$a_1, a_2, \dots, a_n$$$ good if $$$a_i \neq i$$$ for each $$$i$$$. Let $$$F(a)$$$ be the number of pairs $$$(i, j)$$$ ($$$1 \le i < j \le n$$$) such that $$$a_i + a_j = i + j$$$. Let's say that an array $$$a_1, a_2, \dots, a_n$$$ is excellent if: - $$$a$$$ is good; - $$$l \le a_i \le r$$$ for each $$$i$$$; - $$$F(a)$$$ is the maximum possible among all good arrays of size $$$n$$$. Given $$$n$$$, $$$l$$$ and $$$r$$$, calculate the number of excellent arrays modulo $$$10^9 + 7$$$. Input Format: The first line contains a single integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases. The first and only line of each test case contains three integers $$$n$$$, $$$l$$$, and $$$r$$$ ($$$2 \le n \le 2 \cdot 10^5$$$; $$$-10^9 \le l \le 1$$$; $$$n \le r \le 10^9$$$). It's guaranteed that the sum of $$$n$$$ doesn't exceed $$$2 \cdot 10^5$$$. Output Format: For each test case, print the number of excellent arrays modulo $$$10^9 + 7$$$. Note: In the first test case, it can be proven that the maximum $$$F(a)$$$ among all good arrays $$$a$$$ is equal to $$$2$$$. The excellent arrays are: 1. $$$[2, 1, 2]$$$; 2. $$$[0, 3, 2]$$$; 3. $$$[2, 3, 2]$$$; 4. $$$[3, 0, 1]$$$.