Find Kth Largest XOR Coordinate Value

Given an m×n matrix, compute for each coordinate (a,b) the XOR of all elements in the submatrix from (0,0) to (a,b) (2D prefix XORs) and return the k-th largest value among these m·n results. The challenge is to efficiently compute all prefix XORs (O(mn)) and select the k-th largest from up to 10^6 values (e.g., via a size-k min-heap or selection algorithm).