A Zero Sum Game Theory

Time Limit: 3 Seconds    Memory Limit: 65536 KB

There are n students involved in a peer review about their course projects. Each student has to score the other n-1 students' projects separately. The score given must be an integer ranging from 0 to 100 (both inclusive), and the final score of a student is the sum of the scores his project receives.

 

But these students are on bad terms with each other, so they all want to minimize the sum of the final scores of the other students, and maximize their own final score when the first condition is satisfied.

 

If every student uses the best strategy, can you predict their final scores?

 

 

Input

There are multiple test cases. The first line of the input contains an integer T ≤ 128, indicating the number of test cases. For each test case, the first and only line contains one integer 2 ≤ n ≤ 128, indicating the number of students involved in the peer review.

 

Output

For each test case output one line containing n integers separated by one space, indicating the final scores of each student. You should print the answer in non-descending order.

Do not output extra spaces at the end of each line.

Sample Input

1
2

Sample Output

0 0

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