colsum rowsum populating matrix

I'm trying to write for each cell entry in a matrix what value is smallest, either its rowsum value or colsum value in a new matrix of the same dimension.

For example:

say I have matrix c which looks like this:

x <- matrix(seq(1:6),2)
x
      [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6

Its rowsum and colsum are:

rowSums(x)
[1]  9 12
colSums(x)
[1]  3  7 11

so based on that info, the new matrix should look like this:

      [,1] [,2] [,3]
[1,]    3    7    9
[2,]    3    7    11

I've been thinking about using apply but I do not know how I can write an if statement to write the smallest value from either rowsum or colsum for each cell entry. Any ideas?