D. Excellent Arraystime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputLet'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.InputThe 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.OutputFor each test case, print the number of excellent arrays modulo 10^9 + 7.ExampleInput
4
3 0 3
4 -3 5
42 -33 55
69 -42 146
Output
4
10
143922563
698570404
NoteIn 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:   [2, 1, 2];  [0, 3, 2];  [2, 3, 2];  [3, 0, 1]. 
4
3 0 3
4 -3 5
42 -33 55
69 -42 146

4 10 143922563 698570404 
['binary search', 'combinatorics', 'constructive algorithms', 'implementation', 'math', 'sortings', 'two pointers', '*2300']