Undergrad Major for MS in Financial Engineering?

Just like the title implies, I’m looking for some insight on what major would be more beneficial to pursue an MS in Financial Engineering. The majors interest to me are:
Business Economics
Math/Econ
Computer Science and Engineering

I feel like Business Economics would in no way prepare me for FE, but it was my first top choice. Just want some insight on this. Any help or suggestions would be grateful.

A quick blurb from Columbia’s MS in financial engineering program:

Financial Engineering is a multidisciplinary field involving financial theory, the methods of engineering, the tools of mathematics and the practice of programming.

and

Students entering the MS in Financial Engineering program should have an appropriate mathematical background in probability, calculus and linear algebra.

They provide a [url=<a href=“http://ieor.columbia.edu/files/seasdepts/industrial-engineering-operations-research/pdf-files/MSFE_Prereq.pdf%5Ddocument%5B/url”>http://ieor.columbia.edu/files/seasdepts/industrial-engineering-operations-research/pdf-files/MSFE_Prereq.pdf]document[/url] with problems they believe that you should be able to solve in order to be competitive.

Based on that answer, for Columbia and other similar financial engineering programs, it seems like a major program of study that is heavy on mathematical, engineering, and computer science elements will prepare you best. A math/econ joint major could do that (particularly if you took a few classes in computer programming); a computer science/engineering program could do it (as long as you made sure to take the requisite courses in calculus and probability/statistics). A business economics major wouldn’t prepare you alone; you’d have to make sure that you took additional coursework in the other fields (calculus & statistics and programming) in order to prepare.

I’m not affiliated with this program, but just based on having looked at similar programs, I would imagine that someone with a heavy quant/computer science/engineering background but very little finance background would actually be more competitive than someone with a heavy business/finance background but with very little experience with programming/advanced math/engineering.