Consider an instance of graph $G=\{V,E\}$ for the shortest

path problem where negative weights are allowed. A

graph $G^{\text{'}}$ is constructed from $G$ by adding a large enough

positive constant $M$ to all edge weights, so that

all weights are now positive in G$\text{'}.$ If the shortest

path $P($from $s$ to $t)$ in $G^{\text{'}}$ is determined using

Djikstra's algorithm, will P be shortest path $($from s to

t$)$ for G as well. If yes, prove; otherwise, give a counter

example.