Problem

You are given two integer arrays A and B of lengths N and M, respectively. Some elements of the arrays are equal to 0. You may replace every 0 with any positive integer. Determine the minimum possible value S such that, after replacing all zeros, both arrays have the same total sum S. If it is impossible, print -1.

Input

N M A1 A2 ... AN B1 B2 ... BM

Output

Print the minimum equal sum, or -1 if no valid assignment exists.