Excellent Arrays

Let's call an integer array a_1, a_2, ..., a_n good if a_i ≠ i for each i.

Let F(a) be the number of pairs (i, j) (1 ≤ i < j ≤ n) such that a_i + a_j = i + j.

Let's say that an array a_1, a_2, ..., a_n is excellent if:

• a is good;
• l ≤ a_i ≤ 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

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first and only line of each test case contains three integers n, l, and r (2 ≤ n ≤ 2 ⋅ 10^5; -10^9 ≤ l ≤ 1; n ≤ r ≤ 10^9).

It's guaranteed that the sum of n doesn't exceed 2 ⋅ 10^5.

Output

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

Example

Input

4 3 0 3 4 -3 5 42 -33 55 69 -42 146

Output

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].

inputFormat

Input

The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first and only line of each test case contains three integers n, l, and r (2 ≤ n ≤ 2 ⋅ 10^5; -10^9 ≤ l ≤ 1; n ≤ r ≤ 10^9).

It's guaranteed that the sum of n doesn't exceed 2 ⋅ 10^5.

outputFormat

Output

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

Example

Input

4 3 0 3 4 -3 5 42 -33 55 69 -42 146

Output

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].

样例

4
3 0 3
4 -3 5
42 -33 55
69 -42 146

4
10
143922563
698570404

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