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문제

Little Q is enjoying hot pot together with Tangjz. There are $n$ dishes of meat in the boiling water, labeled by $1,2,\dots,n$. The $i$-th dish of meat will be ready at moment $a_i$, and it will take Little Q $b_i$ units of time to fully eat it. Little Q can start eating dish $i$ at any moment $t \geq a_i$, and then he has to eat it until moment $t + b_i$. Little Q can't be eating more than one dish of meat at the same time.

Little Q is called "King of Hot Pot", and he wants to show off before Tangjz by fully eating $k$ dishes of meat as soon as possible. The timer starts at moment $0$. Please write a program to help Little Q, for each $k$ independently ($1 \leq k \leq n$), find $k$ dishes of meat and the order to eat them such that the total time before he fully eats $k$ dishes is minimized. Note that any waiting time is also included in the answer.

입력

The first line contains a single integer $T$ ($1 \leq T \leq 10\,000$), the number of test cases. For each test case:

The first line contains an integer $n$ ($1 \leq n \leq 300\,000$) denoting the number of dishes of meat.

Each of the following $n$ lines contains two integers $a_i$ and $b_i$ ($1 \leq a_i, b_i \leq 10^9$) describing a dish of meat.

It is guaranteed that the sum of all $n$ is at most $1\,000\,000$.

출력

For each test case, output a single line containing $n$ integers, the $k$-th ($1 \leq k \leq n$) of which is the minimum total time before Little Q can fully eat $k$ dishes of meat.

예제 입력 1

1
5
1 2
4 6
3 5
4 2
3 2

예제 출력 1

3 5 7 12 18