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:
Given $$$n$$$, $$$l$$$ and $$$r$$$, calculate the number of excellent arrays modulo $$$10^9 + 7$$$.
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 $$$2 \cdot 10^5$$$.
For each test case, print the number of excellent arrays modulo $$$10^9 + 7$$$.
4 3 0 3 4 -3 5 42 -33 55 69 -42 146
4 10 143922563 698570404
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:
Name |
---|