Two Tables

You've got two rectangular tables with sizes n_a × m_a and n_b × m_b cells. The tables consist of zeroes and ones. We will consider the rows and columns of both tables indexed starting from 1. Then we will define the element of the first table, located at the intersection of the i-th row and the j-th column, as a_i, j; we will define the element of the second table, located at the intersection of the i-th row and the j-th column, as b_i, j.

We will call the pair of integers (x, y) a shift of the second table relative to the first one. We'll call the overlap factor of the shift (x, y) value:

where the variables i, j take only such values, in which the expression a_i, j·b_{i + x, j + y} makes sense. More formally, inequalities 1 ≤ i ≤ n_a, 1 ≤ j ≤ m_a, 1 ≤ i + x ≤ n_b, 1 ≤ j + y ≤ m_b must hold. If there are no values of variables i, j, that satisfy the given inequalities, the value of the sum is considered equal to 0.

Your task is to find the shift with the maximum overlap factor among all possible shifts.