High execution time to count overlapping substrings

I was doing this HackerRank problem which basically boils down to counting overlapping substrings in a string. I used this solution from StackOverflow to build this program -

def overlapping_occurrences(string, sub):
count = start = 0
while True:
start = string.find(sub, start) + 1
if start > 0:
count+=1
else:
return count

def find_health(start, end, d, genes, gene_health):
hv = 0
beneficial = set(genes[start:end+1])
for b in beneficial:
# b is just a single letter, so no possibilities of overlapping
if len(b) == 1:
occurrences = d.count(b)
else:
occurrences = overlapping_occurrences(d, b)
total_value = sum(gene_health[b])
hv += total_value*occurrences
return hv

if __name__ == '__main__':
n = int(raw_input())
genes = list(raw_input().split())
health = list(raw_input().split())
gene_health = {}
for idx in xrange(n):
try:
gene_health[genes[idx]].append(int(health[idx]))
except:
gene_health[genes[idx]] = []
gene_health[genes[idx]].append(int(health[idx]))
s = int(raw_input())
health_values = []
for _ in xrange(s):
start, end, d = raw_input().split()
health_values.append(find_health(int(start), int(end), d, genes, gene_health))
low = min(health_values)
high = max(health_values)
print "%d %d" % (low, high)

I've used a dictionary gene_health because as the first example in the problem description shows, a single gene can have multiple different values, so I store all those values in a list which I sum over to get the total_value.

My problem is that this program takes a very long time and exceeds the time limit on most of the test cases. I do think that this algorithm is CORRECT, since for the few test cases where it doesn't time out, it gives the correct answer. So I'm just looking for a way to speed up the program, and I think the only place where any speedups can be performed is in the overlapping_occurrences method.

I've searched for other similar questions on StackOverflow but all of them use regex but regex will make it even slower (I think).

Any suggestions or poking in the right direction will help. Thank you!

overlapping_occurrences has $O(MN)$ complexity where $M$ and $N$ are the sizes of the string and the substring respectively. You can reduce it to $O(M+N)$ using KMP algorithm. However, looking at the constraints, I feel that even that might not be sufficient - the highest score for the problem is only 50.