One day when I had my math class,I came up with an idea.But I found that I can't solve it.

After class I asked many people but they did't solve it too.

Here's the problem:

You are given a undirected weighted graph with n nodes and m edges.

You need to find a simple path from 1 to n to maximize the maximum value of edges in the path minus the minimum one.

A simple path means that you can't pass through one edge twice or more.

(I don't know how large n,m can be)

Update:Thanks to TimonKnigge,we can solve it in $$$O(m^3)$$$

Update:Thanks to aleex,we can solve it in $$$O(m\log m\log \max value)$$$