Finding values in consecutive rows in R

An example of the dataframe I have is given below.

ID     X      
1      1     
2      2      
3      1      
4      0      
5      0      
6      1      
7      4
8      5 
9      6
10     7
11     0 
12     0

I want to apply logic to it that looks to see whether 3 or more consecutive rows have a value >0 in it. If they do I want to flag them in another column. Hence the output will look as follows.

ID     X      Y
1      1      1
2      2      1
3      1      1
4      0      0
5      0      0
6      1      1
7      4      1
8      5      1
9      6      1
10     7      1
11     0      0
12     0      0