Richard is a penguin running a lockout tournament for ~N~ students who are vying to qualify for CCO.

The students are seeded from ~1~ to ~N~, and every pair of students will face off in a match where either the match ends in a tie or one student wins, and the other loses.

In the event of a tie, both students earn ~b~ points. Otherwise, the winner earns ~a~ points, and the loser earns ~c~ points.

Students are then ranked in decreasing order by their number of points. Students who are tied by points are ranked in increasing order by seed.

For given values of ~N~, ~K~, ~a~, ~b~, and ~c~, compute the maximum and minimum number of points that the student ranked ~K~th can have.

Constraints

~1 \le T \le 10^5~

~1 \le K \le N \le 10^9~

~0 \le a, b, c \le 10^9~

In tests worth 3 marks, ~b = 0~ and ~c = 0~.

In tests worth an additional 3 marks, ~b = 0~.

In tests worth an additional 3 marks, ~c = 0~.

Input Specification

The first line contains a single integer, ~T~.

The next ~T~ lines contain five integers, ~N~, ~K~, ~a~, ~b~, and ~c~.

Output Specification

Output ~T~ lines. On the ~i~th line, output two integers, the maximum and minimum number of points the ~K~th ranked student can have.

Sample Input

1
4 1 3 1 0

Sample Output

9 3