18605번 - Coins 다국어

There are n groups of coins, and the i-th group contains two coins valued as a_i and b_i. Now you want to pick exactly k coins out of them. However, there is a restriction: you can not pick the second coin (the one valued as b_i) in the i-th group without picking the other one in the same group. In other words, in the i-th group, you can:

• pick none of the two coins;
• pick only the first one valued as a_i; or
• pick both of them.

Let f(k) be the maximum total value if we pick exactly k coins.

Find the values f(1), f(2), . . . , f(2n).

The input contains several test cases, and the first line contains a single integer T (1 ≤ T ≤ 90), the number of test cases.

For each test case, the first line contains an integer n (1 ≤ n ≤ 100 000), indicating the number of coin groups.

Each of the following n lines contains two integers a_i and b_i (1 ≤ a_i, b_i ≤ 10 000) indicating the coin values in that group.

It is guaranteed that the sum of n in all test cases does not exceed 2 100 000.

For each test case, just output 2n integers on a single line representing f(1), f(2), . . . , f(2n). Separate consecutive integers by single spaces.