Obtaining B from A

Karthikeya challenged Bappa with a very tricky problem. The problem is quoted below: You are given two array $A$ and $B$ of size $N$. You can perform the following operation on array $A$ - select three different indices ($1$-based indexing) $i$, $j$, $k$ $(1 \leq i,j,k \leq N)$ such that $i+j == k$ and increment values at $i$ and $j$ by $1$ and decrement the value at $k$ by $1$. Determine whethe