Problem C

Expression Again

Input: standard input
Output: standard output

Time Limit: 6 seconds

You are given an algebraic expression of the form (x1+x2+x3+.....+xn)*(y1+y2+.........+ym) and (n+m) integers. You have to find the maximum and minimum value of the expression using the given integers. For example if you are given (x1+x2)*(y1+y2) and you are given 1, 2, 3 and 4. Then maximum value is (1+4)*(2+3) = 25 whereas minimum value is (4+3)*(2+1) = 21.

Input

Each input set starts with two positive integers N, M (less than 51). Next line follows (N+M) integers which are in the range of -50 to 50. Input is terminated by end of file. There will be atmost 110 testcases.

Output

Output is one line for each case, maximum value followed by minimum value.

Sample Input Output for Sample Input

2 2

1 2 3 4

3 1

1 2 3 4

2 2

2 2 2 2

25 21

24 9

16 16

Problem setter: Md Kamruzzaman, Member of Elite Problemsetters' Panel

Input

Output

Sample Input Output for Sample Input

Special Thanks: Monirul Hasan, Md. Sajjad Hossain