Large function excluding a specific value

I have the following large function that finds the next number (in the range A1:I1) below the value in (L1). E.g. range: 1,4,8,12,32,50,51,55,61 - L1=40 - so this would output 32 which is the next number in the range below 40.

=LARGE(A1:I1,COUNTIF(A1:I1,">"&L1)+1)

I need to exclude a specific value that would reside in cell M1, e.g. 32, so given the example above the large formula would output 12 because the next value below 40, excluding 32, is 12. Can anyone help exclude a specific value without compromising what this formula already does?

Appreciation in advance