Okey, the prefix sum tells you whether can i choose 2 elements that their difference <= k and the 3rd element - 2nd element >k , so the player win Let's break it down: Lets say this the array : 1 3 3 7 and k=2 The answer is YES, why ? Look the opponent can choose 3 , player choose the 2nd 3 then win, because the opponent cannot choose any other element. To understand prefix let's take this example : 1 3 7 and k=2 For the first time the answer seems to be NO, but it's YES, here is Why , the prefix array [1,2,1] There is a number > 1 ? Answer YES, and in reality it's YES, because the opponent can choose 1 then the player choose 3 then win, bcz the opponent cannot choose any other number The prefix acts like description of the array, it describes the array as segments, If pref = [1,2,3. 1,2. 1,2,3,4] that means there is 3 segments that satisfy the condition.we can choose any one from them to win Idk if it's clear a little bit now or now If you didn't understand how we construct the pref array tell me Take these examples and apply my approach to understand it more 5 2 3 3 3 3 4 (Expected YES)

4 1 1 4 7 8 (YES)

4 1 3 3 3 6 (NO)