Types: N: int, M: int, X: int, Y: int, a: List[int], b: List[int]
Ranges: 6 ≤ N ≤ 6000, 0 ≤ M ≤ N, 0 ≤ X ≤ 6, 0 ≤ Y ≤ 12, 1 ≤ a_i ≤ 6000, 1 ≤ b_i ≤ 3000, 1 ≤ a_i-b_i ≤ 3000
Addtl Info: 2X + Y = 12, X + Y ≤ N, X ≤ M