codeforces#P1550D. Excellent Arrays

    ID: 32234 远端评测题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 8 上传者: 标签>combinatoricsconstructive algorithmsimplementationmathtwo pointers*2300

Excellent Arrays

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 $10^9 + 7$.

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 $10^9 + 7$.

Input

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

For each test case, print the number of excellent arrays modulo $10^9 + 7$.

Samples

4
3 0 3
4 -3 5
42 -33 55
69 -42 146
4
10
143922563
698570404

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. $[3, 0, 1]$.