P4862 Number Guessing.

Iris and Beryl are playing a number guessing game.

The game works as follows: given a positive integer $n$, Iris chooses a number $m$ from $S=\{1,2,...,n\}$. Then, Iris must answer Beryl’s questions truthfully. Each question is of the form: “Is $m$ an element of set $A$?” where $A\subseteq S$. If Iris answers “Yes”, then Beryl must give Iris $a$ yuan; otherwise, Beryl must give Iris $b$ yuan. (The testdata guarantees $a>b$.) How much money does Beryl need to prepare at least, to be sure that she can determine the number in Iris’s mind?

The first line contains two positive integers $a$ and $b$, and the number of test cases $t$. The next $t$ lines each contain a given positive integer $n$, with the meaning as described above.

Output $t$ lines. For each test case, output the minimum amount of money Beryl needs to prepare.

[Explanation for the 1st test case of Sample 1] Beryl first asks about the set $\{1\}$. If the answer is “Yes”, then Iris’s number is confirmed to be $1$, and Beryl needs $2$ yuan. If the answer is “No”, then Beryl asks about the set $\{2\}$. Clearly, in the worst case she needs to spend another $2$ yuan, for a total of $3$ yuan, so the answer is $3$ yuan. ---- [Constraints] | Test Point ID | $n$ | $t$ | $a$,$b$ | | :----------- | :----------- | :----------- | :----------- | | 1 | $\leq 20$ | $\leq 10$ | $\leq 20$ | | 2 | $\leq 20$ | $\leq 10$ | $\leq 20$ | | 3 | $\leq 2000$ | $\leq 100$ | $\leq 500$ | | 4 | $\leq 2000$ | $\leq 100$ | $\leq 500$ | | 5 | $\leq 2000$ | $\leq 100$ | $\leq 500$ | | 6 | $\leq 2000$ | $\leq 100$ | $\leq 500$ | | 7 | $\leq 2000$ | $\leq 100$ | $\leq 500$ | | 8 | $\leq 10^{18}$ | $\leq 200$ | $a=2$,$b=1$ | | 9 | $\leq 10^{18}$ | $\leq 200$ | $a=2$,$b=1$ | | 10 | $\leq 10^{18}$ | $\leq 200$ | $a=2$,$b=1$ | Translated by ChatGPT 5