Given inputs as positive integers $a$,$b$, and $c(i,j)$ where $i,j\leq a$, decide if there is a permutation $\tau$ such that

Question

Given inputs as positive integers $a$,$b$, and $c(i,j)$ where $i,j\leq a$, decide if there is a permutation $\tau$ such that $$c(\tau(a),\tau(1))+\sum_{i=1}^{a-1} c(\tau(i),\tau(i+1))\leq b $$ Prove this problem is NP-complete.

The NP-complete problems I have studied are SAT, nSAT, Hamiltonian path and partition sum. The problem looks like an Hamiltonian problem but I am not sure how to connect them. Can anyone give me a hint?