Puzzles #139 & #140 - Fix It In Post (Icelom)

Icelom is a rare but very interesting puzzle type. Both of these puzzles were made with faulty assumptions- one in the rules, and one as a deduction, and so both have a different variant because of course they do.

puzz.link interface    penpa interface (answer check)

The answer checker checks for > instead of the more interesting >=. For this puzzle, all standard rules apply, and all numbers along the path must be greater than or equal to all previous numbers on the path.

puzz.link interface

This one, on the other hand, was one that I thought worked as a vanilla Icelom, but later realized I was mistaken. In this puzzle, all standard rules apply. Additionally, all ice cells must be used (not just white cells).