#10690Expression Again

You are given an algebraic expression of the form (x₁ + x₂ + x₃ + . . . + x_n) ∗ (y₁ + y₂ + . . . + y_m) 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 where as minimum value is (4 + 3) ∗ (2 + 1) = 21.

Input

Each input set starts with two positive integers N , M (< 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.

2 2
1 2 3 4
3 1
1 2 3 4
2 2
2 2 2 2

25 21
24 9
16 16