P6400 [COI 2008] UMNOZAK

Define the digit product of a positive integer as the result of multiplying all of its digits. For example: The digit product of $2612$ is: $2\times 6\times 1\times 2=24$. Define the self-product of a positive integer as the result of multiplying the number by its digit product. For example: The self-product of $2612$ is: $2612\times 24=62688$. Given two integers $A,B$, find the number of positive integers whose self-product lies in the interval $[A,B]$.

Input one line containing two integers $A,B$.

Output one line containing one integer, indicating how many positive integers have their self-product within the interval $[A,B]$.

#### Explanation for Sample 2 There are $19,24,32,41$ that satisfy the requirement. Their self-products are $171,192,192,164$, respectively. #### Constraints - For $25\%$ of the testdata, $A\le B\le 10^8$; - For another $15\%$ of the testdata, $A\le B\le 10^{12}$; - For $100\%$ of the testdata, $1\le A\le B< 10^{18}$. #### Notes **This problem is translated from [COCI2007-2008](https://hsin.hr/coci/archive/2007_2008/) [COI2008](https://hsin.hr/coci/archive/2007_2008/olympiad_tasks.pdf) *T4 UMNOZAK***。 Translated by ChatGPT 5