Problem Description

In a football tournament, Team A and Team B played a total of $n$ matches. The tournament uses a point system: the winning team gets $a$ points, the losing team gets $b$ points, and if the match is a draw then both teams get $c$ points each. It is known that Team A scored a total of $d$ goals, and Team B scored a total of $e$ goals. Find the maximum possible total score and the minimum possible total score for Team A.

Input Format

This problem contains multiple test cases.

The first line contains an integer $T$, the number of test cases.

For each test case, input one line with six integers $n,a,b,c,d,e$.

Output Format

For each test case, output one line with two integers separated by a space, representing the maximum possible total score and the minimum possible total score.

5
5 3 0 2 5 2
5 5 2 3 0 5
3 100 1 2 6 6
5 9 0 2 3 9
4 5 0 5 1 3

13 7
14 10
201 6
29 0
15 5

Hint

Sample Explanation

To make the samples easier to understand, the sample explanations for the first three test cases are given below:

In the table, $(x_1,y_1),(x_2,y_2),\cdots,(x_n,y_n)$ means the score of match $1$ is $x_1:y_1$, the score of match $2$ is $x_2:y_2$, and so on.

Constraints

This problem uses bundled testdata.

For all test cases, $1\le T\le 10^5$, $1\le n \le 10^9$, $0\le d,e\le10^9$, $0\le b\le c \le a\le10^9$.

Translated by ChatGPT 5