Stats help, interpreting the output of bedtools fisher

[biocomputer]

Forgive me if this is trivial, I want to make sure I understand the output of bedtools fisher. I've used it to compare several sets of intervals in the human genome and want to say whether two sets of intervals have a statistically significant overlap or not. Here are the abbreviated outputs from 6 tests (I can give the full outputs if needed):

Test   left    right   two-tail        ratio
1:     0       1       0       3.655
2:     1       1.3018e-39      2.5115e-39      1.180
3:     1       4.9869e-47      9.3199e-47      1.198
4:     1       3.7421e-45      6.909e-45       1.194
5:     0.71641	0.40143	0.61502	1.123
6:     0.63306	0.49828	0.86348	1.040

Is it correct that: a small left p-value indicates the intervals overlap significantly more than expected (test #1 above), a small right p-value indicates the intervals overlap significantly less than expected (tests 2,3,4), and if neither the left or right p-values are small (tests 5,6) the intervals overlap "randomly" (not sure what the correct term is, basically they don't overlap more or less than would be expected)? Also I don't understand how to interpret the two-tail p-value and ratio for these tests. Thank you to anyone who can help clarify this for me.