AND on Graph

You are given an undirected graph with $n$ nodes and $m$ edges. The nodes are numbered from 1 to $n$. Each edge $e$ of the graph has two integers associated with it, cost($c_e$) and value($v_e$). You are given three integers $s$, $t$, and $K$. The cost of a walk is the sum of costs of all the edges in the walk. Find the minimum cost of a walk from $s$ to $t$ ($s \neq t$), such that the bitwise AN