Mutate variable if certain columns contain string in R

I have been struggling for hours with this dataset. I have searched for hours and tried many things, but I failed (I am a novice in R). So I really hope you guys can help me.

I have this dataset:

      df <- data.frame(ID = c(1,2,3,4,5), a.1 = c("A", "C", "C", "B","D"), a.2 = c("C", "C", "D", "A","B"), b.1 = c("D", "C", "A", "B","D"), b.2 = c("D", "B", "C", "A","A"))
    
  ID a.1 a.2 b.1 b.2
1  1   A   C   D   D
2  2   C   C   C   B
3  3   C   D   A   C
4  4   B   A   B   A
5  5   D   B   D   A

I would like to mutate a new variable called "result" to be:

• "1" if one of the columns with prefix "a." contain "A" or "B"
• "0" if one of the columns with prefix "a." do not contain "A" or "B"

So I would get the following result:

  ID a.1 a.2 b.1 b.2 result
1  1   A   C   D   D      1
2  2   C   C   C   B      0
3  3   C   D   A   C      0
4  4   B   A   B   A      1
5  5   D   B   D   A      1

In my real dataset I have 100 variables with prefix "a.", so I cannot select the columns individually.

Hopefully you guys can help me!

Thank you very much!