Extract row if both column values appear in a single column from a separate file

I have two tab-separated files:

File 1

123 456 135 567 234 478 

File 2

123 notimportant notimportant2 456 notimportant notimportant2 987 notimportant notimportant2 135 notimportant notimportant2 234 notimportant notimportant2 478 notimportant notimportant2 

I need to extract lines from file1 if both entries in a single row are present in file2's first column. So the output file should be like:

Output

123 456 234 478 

I previously used this awk command to extract rows if only the first column of file1 matched 1st column of file2

awk 'FNR==NR{a[$1];next}($1 in a){print}' file2 file1 

But I don't know how to expand it.