201310: [AtCoder]ARC131 A - Two Lucky Numbers

Problem Statement

Mr. AtCoder reads in the newspaper that today's lucky number is a positive integer $A$ and tomorrow's is a positive integer $B$.

Here, he defines a positive integer $x$ that satisfies both of the following conditions as a super-lucky number.

• The decimal notation of $x$ contains $A$ as a contiguous substring.
• The decimal notation of $2x$ contains $B$ as a contiguous substring.

Actually, under the Constraints of this problem, there is always a super-lucky number less than $10^{18}$. Find one such number.

Constraints

• $1 \leq A < 10^8$
• $1 \leq B < 10^8$
• $A$ and $B$ have no leading 0s.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$A$
$B$

Output

Print one super-lucky number less than $10^{18}$. If multiple solutions exist, you may print any of them.

Sample Input 1

13
62

Sample Output 1

131

One super-lucky number is $x = 131$, because:

• $x = 131$ contains $13$ as a substring. ($1$-st through $2$-nd characters)
• $2x = 262$ contains $62$ as a substring. ($2$-nd through $3$-rd characters)

Some other super-lucky numbers are $313$, $8135$, and $135797531$, which would also be accepted.

Sample Input 2

69120
824

Sample Output 2

869120

One super-lucky number is $x = 869120$, because:

• $x = 869120$ contains $69120$ as a substring. ($2$-nd through $6$-th characters)
• $2x = 1738240$ contains $824$ as a substring. ($4$-th through $6$-th characters)

The smallest super-lucky number is $69120$, but note that any lucky number with at most $18$ digits would be accepted.

Sample Input 3

6283185
12566370

Sample Output 3

6283185

When $x = 6283185$, $x$ is $A$ itself, and $2x$ is $B$ itself. In such a case too, $x$ is a super-lucky number.