[Solution] Yet Another Chef And Numbers CodeChef Solution

Problem

Chef is again playing with numbers.

He defines the rating of a number as the count of trailing zeros in the product of all the digits of the number.

Chef wants you to find the sum of ratings of all the numbers between the numbers $A$ and $B$ (excluding $A$). As the answer can be very large, print it modulo $10^9+7$.

Note: If the product of the digits of a number is $0$, the number's rating is defined to be $1$.

Input Format

• The first line contains $2$ space-separated integers, $A$ and $B$.

Output Format

Output a single integer, the sum of ratings of all the numbers between the numbers $A$ and $B$ (excluding $A$). As the answer can be very large, print it modulo $10^9+7$.

Explanation:

$10$ will have rating $1$ as its product of digits = $1 \cdot 0$ = $0$ has $1$ trailing zero. All other numbers have a single digit and

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 thus, no trailing zeroes.

Explanation:

Chef will rate $20,25,$ and $30$ as $1$ as the product of their digits have $1$ trailing zeros. All other numbers have no trailing zeroes.

Explanation:

The product of digits of $455$ is $4\cdot 5\cdot 5 = 100$, which has $2$ trailing zeroes. Thus, the rating is $2$.