P16872 [GKS 2022 #A] Interesting Integers

Let us call an integer *interesting* if the product of its digits is divisible by the sum of its digits. You are given two integers $A$ and $B$. Find the number of interesting integers between $A$ and $B$ (both inclusive).

The first line of the input gives the number of test cases, $T$. $T$ lines follow. Each line represents a test case and contains two integers: $A$ and $B$.

For each test case, output one line containing `Case` $\#x$: $y$, where $x$ is the test case number (starting from $1$) and $y$ is the number of interesting integers between $A$ and $B$ (inclusive).

In Sample Case #$1$, since the product and the sum of digits are the same for single-digit integers, all integers between $1$ and $9$ are interesting. In Sample Case #$2$, there are no interesting integers between $91$ and $99$. In Sample Case #$3$, there are $5$ interesting integers between $451$ and $460$: 1. $451$ (product of its digits is $4 \times 5 \times 1 = 20$, sum of its digits is $4 + 5 + 1 = 10$). 2. $453$ (product of its digits is $4 \times 5 \times 3 = 60$, sum of its digits is $4 + 5 + 3 = 12$). 3. $456$ (product of its digits is $4 \times 5 \times 6 = 120$, sum of its digits is $4 + 5 + = 15$). 4. $459$ (product of its digits is $4 \times 5 \times 9 = 180$, sum of its digits is $4 + 5 + 9 = 18$). 5. $460$ (product of its digits is $4 \times 6 \times 0 = 0$, sum of its digits is $4 + 6 + 0 = 10$). ### Limits $1 \le T \le 100$. **Test Set $1$** $1 \le A \le B \le 10^5$. **Test Set $2$** $1 \le A \le B \le 10^{12}$.