Binary search on the answer

Return minimum capacity partitioning positive weights in original order into at most days nonempty contiguous groups. Empty weights return 0 for positive days. days<=0 or any weight<=0 throws invalid_argument. Prototype tests capacities; final binary-searches monotone feasibility with O(1) auxiliary state. Preserve input.

Public signatures:

Int prototype(const Vec<Int>& weights,const Int& days);
Int solve(const Vec<Int>& weights,const Int& days);

Compile and run from this directory:

c++ -std=c++20 -O2 -Wall -Wextra -pedantic -pthread main.cpp -o practice
./practice --stage prototype
./practice --stage final

Edit exercise.hpp. Both stages start unfinished and must report failures until implemented. Keep main.cpp as the executable contract. The runner returns nonzero for a failed check, an unexpected exception, an invalid stage, or an empty suite. C++20 and only the standard library are required.