B. A BIT of a Construction

Given integers 𝑛 and 𝑘, construct a sequence of 𝑛 non-negative (i.e. ≥0) integers 𝑎1,𝑎2,…,𝑎𝑛𝑎1,𝑎2,…,𝑎𝑛 such that

1. ∑𝑖=1𝑛𝑎𝑖=𝑘
2. The number of 1s in the binary representation of 𝑎1|𝑎2|…|𝑎𝑛 is maximized, where | denotes the bitwise OR operation.