D. Missing Subsequence Sum

You are given two integers 𝑛 and 𝑘. Find a sequence 𝑎 of non-negative integers of size at most 25 such that the following conditions hold.

• There is no subsequence of 𝑎 with a sum of 𝑘.
• For all 1≤𝑣≤𝑛 where 𝑣≠𝑘, there is a subsequence of 𝑎 with a sum of 𝑣.

A sequence 𝑏 is a subsequence of 𝑎 if 𝑏 can be obtained from 𝑎 by the deletion of several (possibly, zero or all) elements, without changing the order of the remaining elements. For example, [5,2,3] is a subsequence of [1,5,7,8,2,4,3].

It can be shown that under the given constraints, a solution always exists.