101582: [AtCoder]ABC158 C - Tax Increase
Description
Score : $300$ points
Problem Statement
Find the price of a product before tax such that, when the consumption tax rate is $8$ percent and $10$ percent, the amount of consumption tax levied on it is $A$ yen and $B$ yen, respectively. (Yen is the currency of Japan.)
Here, the price before tax must be a positive integer, and the amount of consumption tax is rounded down to the nearest integer.
If multiple prices satisfy the condition, print the lowest such price; if no price satisfies the condition, print -1
.
Constraints
- $1 \leq A \leq B \leq 100$
- $A$ and $B$ are integers.
Input
Input is given from Standard Input in the following format:
$A$ $B$
Output
If there is a price that satisfies the condition, print an integer representing the lowest such price; otherwise, print -1
.
Sample Input 1
2 2
Sample Output 1
25
If the price of a product before tax is $25$ yen, the amount of consumption tax levied on it is:
- When the consumption tax rate is $8$ percent: $\lfloor 25 \times 0.08 \rfloor = \lfloor 2 \rfloor = 2$ yen.
- When the consumption tax rate is $10$ percent: $\lfloor 25 \times 0.1 \rfloor = \lfloor 2.5 \rfloor = 2$ yen.
Thus, the price of $25$ yen satisfies the condition. There are other possible prices, such as $26$ yen, but print the minimum such price, $25$.
Sample Input 2
8 10
Sample Output 2
100
If the price of a product before tax is $100$ yen, the amount of consumption tax levied on it is:
- When the consumption tax rate is $8$ percent: $\lfloor 100 \times 0.08 \rfloor = 8$ yen.
- When the consumption tax rate is $10$ percent: $\lfloor 100 \times 0.1 \rfloor = 10$ yen.
Sample Input 3
19 99
Sample Output 3
-1
There is no price before tax satisfying this condition, so print -1
.