this hard version problem the difference constraint n m t you hack version problem solvedAlice Bob give number n m k play game followsThe game score Alice try maximize Bob tries minimize the score initially 0 the game consist n turn each turn Alice pick real number 0 k inclusive Bob add subtract score game but game Bob choose add m n turnsbob get know number Alice pick decide add subtract number score Alice get know Bob add subtract number previous turn pick number current turn turn previous turnif Alice Bob play optimally final score game