P15263 [USACO26JAN2] Circle of Cows P

Farmer John has $N$ ($2\le N\le 1000$) cows at distinct locations $l_1,\dots, l_N$ along a circle of circumference $C$ ($0\le l_1 < l_2 < \dots < l_N

The first line contains $N$ and $C$. The second line contains $l_1\dots l_N$.

Output a single line with $\lfloor N/2\rfloor$ space-separated integers, with the answers for $k=1\dots \lfloor N/2\rfloor$ in that order.

#### Sample 1 Explanation For $k = 1$, cow 1 can be paired to cow 3, which is distance $50$ away along the circumference of the circle, making the answer $50$. For $k = 2$, cow 1 can be paired to cow 3, and cow 2 can be paired to cow 4, which is distance $50$ away from it along the circumference of the circle, making the answer still $50$. #### Sample 2 Explanation For $k = 1$, cow 3 can be paired to cow 4, which is distance $2 + 100 - 99 = 3$ away from it along the circumference of the circle, making the answer $3$. For $k = 2$, cow 1 can be paired to cow 3 and cow 2 can be paired to cow 4. Each of these pairs contains two cows at a distance of $2$ from each other along the circumference of the circle, making the answer $2$. SCORING: - Inputs 3-4: $2l_N \le C$ - Inputs 5-6: $N\le 20$ - Inputs 7-14: $N\le 100$ - Inputs 15-22: No additional constraints.