B. Move to the End
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given an array $$$a$$$ consisting of $$$n$$$ integers.

For every integer $$$k$$$ from $$$1$$$ to $$$n$$$, you have to do the following:

  1. choose an arbitrary element of $$$a$$$ and move it to the right end of the array (you can choose the last element, then the array won't change);
  2. print the sum of $$$k$$$ last elements of $$$a$$$;
  3. move the element you've chosen on the first step to its original position (restore the original array $$$a$$$).

For every $$$k$$$, you choose the element which you move so that the value you print is the maximum possible.

Calculate the value you print for every $$$k$$$.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Each test case consists of two lines:

  • the first line contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$);
  • the second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$).

Additional constraint on the input: the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, print $$$n$$$ integers. The $$$i$$$-th of these integers should be equal to the maximum value you can print if $$$k=i$$$.

Example
Input
4
7
13 5 10 14 8 15 13
6
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
1
42
2
7 5
Output
15 28 42 50 63 73 78 
1000000000 2000000000 3000000000 4000000000 5000000000 6000000000 
42 
7 12
Note

Let's consider the first test case from the statement:

  • when $$$k = 1$$$, you can move the $$$6$$$-th element to the end, the array becomes $$$[13, 5, 10, 14, 8, 13, 15]$$$, and the value you print is $$$15$$$;
  • when $$$k = 2$$$, you can move the $$$6$$$-th element to the end, the array becomes $$$[13, 5, 10, 14, 8, 13, 15]$$$, and the value you print is $$$13 + 15 = 28$$$;
  • when $$$k = 3$$$, you can move the $$$4$$$-th element to the end, the array becomes $$$[13, 5, 10, 8, 15, 13, 14]$$$, and the value you print is $$$15 + 13 + 14 = 42$$$;
  • when $$$k = 4$$$, you can move the $$$5$$$-th element to the end, the array becomes $$$[13, 5, 10, 14, 15, 13, 8]$$$, and the value you print is $$$14 + 15 + 13 + 8 = 50$$$;
  • when $$$k = 5$$$, you can move the $$$1$$$-st element to the end, the array becomes $$$[5, 10, 14, 8, 15, 13, 13]$$$, and the value you print is $$$14 + 8 + 15 + 13 + 13 = 63$$$;
  • when $$$k = 6$$$, you can move the $$$1$$$-st element to the end, the array becomes $$$[5, 10, 14, 8, 15, 13, 13]$$$, and the value you print is $$$10 + 14 + 8 + 15 + 13 + 13 = 73$$$;
  • when $$$k = 7$$$, you can move the $$$6$$$-th element to the end, the array becomes $$$[13, 5, 10, 14, 8, 13, 15]$$$, and the value you print is $$$13 + 5 + 10 + 14 + 8 + 13 + 15 = 78$$$.