Largest Subsequence Number

You are given three numbers $N$, $Q$, and $R$. Find $M$ that satisfies all of the following.

• $M$ is positive.
• The decimal representation of $M$ is a subsequence of the decimal representation of $N$, so you can build $M$ by deleting zero or more digits of $N$.
• $M$ leaves a remainder of $R$ when divided by $Q$.
• $M$ is the largest value that satisfies the conditions.

A decimal representation does not start with 0, so the first digit you keep cannot be 0.

The first line contains the number of test cases $T$ ($1 \le T \le 200$). Each of the next $T$ lines contains one test case.

Each line has three integers separated by single spaces, $N$, $R$, and $Q$, in this order ($1 \le N < 10^{1000}$, $0 \le R < Q \le 1000$). No number in the input has a leading zero.

For each test case, print the $M$ described above on a single line, with no leading zeros. If no such $M$ exists, print Not found on a single line instead.

For $N = 840$, $R = 0$, $Q = 8$, the number $840$ is divisible by $8$, so the largest $M$ is $840$.

For $N = 901$, $R = 3$, $Q = 8$, the subsequences of $901$ are $9$, $0$, $1$, $90$, $01$, $91$, $901$. Among them $0$ is not positive and $01$ has a leading zero, so both drop out. Of the rest, only $91$ leaves a remainder of $3$ when divided by $8$.

For $N = 123456789$, $R = 10$, $Q = 100$, no subsequence leaves a remainder of $10$ when divided by $100$.