Initially, there is a magical stone of mass 2^{N} lying at the origin of the number line. For the next N seconds, the following event happens:

Let us define the decomposition of a magical stone as follows: If there is a magical stone of mass M > 1 lying at coordinate X, then it decomposes into two magical stones, each of mass $\frac{M}{2}$ lying at the coordinates X-1 and X+1 respectively. The original stone of mass M gets destroyed in the process.
Each second, all the magical stones undergo decomposition simultaneously.

Note that there can be more than one stone at any coordinate X.

Given a range [L, R], find out the number of stones present at each of the coordinates in the range [L, R]. As the number of stones can be very large, output them modulo (10^{9} + 7).

------ Input Format ------

• The first line contains a single integer T - the number of test cases. Then the test cases follow.
• The first and only line of each test case contains three integers N, L and R, as described in the problem statement.

------ Output Format ------

For each testcase, output in a single line a total of (R-L+1) space-separated integers. The i^{th} integer will denote the number of stones present at X = (L+i-1) coordinate.
As the number of stones can be very large, output them modulo (10^{9} + 7).

------ Constraints ------

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 10^{6}$
$-N ≤ L ≤ R ≤ N$
- Sum of $(R-L+1)$ over all the test cases doesn't exceed $10^{5}$.

----- Sample Input 1 ------
3
2 -2 2
2 0 2
150000 48 48

----- Sample Output 1 ------
1 0 2 0 1
2 0 1
122830846

----- explanation 1 ------
Test case 1: Let us look at the number of stones for $x = -2$ to $x = 2$ as the time progresses:

$t = 0$: $\{0, 0, 1, 0, 0\}$

$t = 1$: $\{0, 1, 0, 1, 0\}$

$t = 2$: $\{1, 0, 2, 0, 1\}$

We have to output the number of stones at $x = -2$ to $x = 2$, which is $\{1, 0, 2, 0, 1\}$.

Test case 2: Similar to first test case, We have to output the number of stones at $x = 0$ to $x = 2$, which is $\{2, 0, 1\}$.

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