Abbreviating the Product of a Range.py

class Solution:
    def abbreviateProduct(self, left: int, right: int) -> str:
        c2 = c5 = 0
        top12 = tail5 = 1

        for i in range(left, right+1):
            # count and remove all 2 and 5
            while i % 2 == 0:
                i //= 2
                c2 += 1
            while i % 5 == 0:
                i //= 5
                c5 += 1

            # track top 12 and last 5
            top12 = int(str(top12 * i)[:12])
            tail5 = tail5 * i % 100000
        
        # multiply the remained 2 or 5
        if c2 > c5:
            for _ in range(c2 - c5):
                top12 = int(str(top12 * 2)[:12])
                tail5 = tail5 * 2 % 100000
        elif c2 < c5:
            for _ in range(c5 - c2):
                top12 = int(str(top12 * 5)[:12])
                tail5 = tail5 * 5 % 100000

        zero = min(c2, c5)

        # as is included in top 12, it's easy to tell when d<=10
        if len(str(top12))<=10:
            return str(top12)+'e'+str(zero)
        
        return str(top12)[:5] + '.'*3 + '0'*(5-len(str(tail5)))+str(tail5)+'e'+str(zero)