Minimum Racks to Pack Machines with Two Resource Constraints

Problem You are given a list of N machines. The i-th machine consumes two types of resources (x_i, y_i). Each rack has two capacity limits (a, b). For any rack, the sum of x requirements of machines placed on it must be <= a, and the sum of y requirements must be <= b. You must assign every machine to exactly one rack (unlimited racks available). Compute the minimum number of racks needed to fit all machines. I/O (suggested) Input: integer N, followed by N pairs (x_i, y_i), and capacities a, b. Output: the minimum number of racks (integer). Constraints / Notes x_i, y_i, a, b are non-negative integers. If there exists an i such that x_i > a or y_i > b, then packing is impossible (return -1 or as specified). Example 1 N = 3 machines: (2,3), (3,2), (2,2) rack capacity: (5,5) Optimal packing: rack1: (2,3) + (3,2) => (5,5) rack2: (2,2) Output: 2 Example 2 N = 4 machines: (4,1), (4,1), (1,4), (1,4) capacity: (5,5) Optimal packing: rack1: (4,1) + (1,4) => (5,5) rack2: (4,1) + (1,4) => (5,5) Output: 2 Example Input 3 2 3 3 2 2 2 5 5 Output 2