Migrated from Lutece 553 Awkward Digits

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Description

Bessie the cow is just learning how to convert numbers between different bases, but she keeps making errors since she cannot easily hold a pen between her two front hooves.

Whenever Bessie converts a number to a new base and writes down the result, she always writes one of the digits wrong. For example, if she converts the number $14$ into binary (i.e., base $2$), the correct result should be 1110, but she might instead write down 0110 or 1111. Bessie never accidentally adds or deletes digits, so she might write down a number with a leading digit of 0 if this is the digit she gets wrong.

Given Bessie's output when converting a number $N$ into base $2$ and base $3$, please determine the correct original value of $N$ (in base $10$). You can assume $N$ is at most $1$ billion, and that there is a unique solution for $N$.

Please feel welcome to consult any on-line reference you wish regarding base-$2$ and base-$3$ numbers, if these concepts are new to you.

Input

• Line $1$: The base-$2$ representation of $N$, with one digit written incorrectly.
• Line $2$: The base-$3$ representation of $N$, with one digit written incorrectly.

Output

• Line $1$: The correct value of $N$.

Samples

1010
212

14

Resources

USACO Nov 2011