We can assume m=k*n+x. So
              m^e mod n = c
          <->(k*n+x)^e mod n = c
          <-> x^e mod n = c
=> We can find m in [1, n] : m^e mod n = c
=> My algorithm run in O(nlogn). Is it fast enough? (because it TLE on test#1)
Explain me!

I don't think it's fast enough.