8291: Awkward Digits

奶牛贝茜正在学习如何在不同进制之间转换数字。


但是她总是犯错误，因为她无法轻易的用两个前蹄握住笔。


每当贝茜将数字转换为一个新的进制并写下结果时，她总是将其中的某一位数字写错。


例如，如果她将数字 14 转换为二进制数，那么正确的结果应为 1110，但她可能会写下 0110 或 1111。


贝茜不会额外添加或删除数字，但是可能会由于写错数字的原因，写下包含前导 0 的数字。


给定贝茜将数字 N 转换为二进制数字以及三进制数字的结果，请确定 N 的正确初始值（十进制表示）。


输入格式
第一行包含 N 的二进制表示，其中一位是错误的。


第二行包含 N 的三进制表示，其中一位是错误的。


输出格式
输出正确的 N 的值。


数据范围
0≤N≤109，且存在唯一解。


输入样例：
1010
212
输出样例：
14
样例解释
14 在二进制下的正确表示为 1110，在三进制下的正确表示为 112。

Problem 2: Awkward Digits [Brian Dean]


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.


PROBLEM NAME: digits


INPUT FORMAT:


* 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.


SAMPLE INPUT (file digits.in):


1010
212


INPUT DETAILS:


When Bessie incorrectly converts N into base 2, she writes down
"1010".  When she incorrectly converts N into base 3, she writes down "212".


OUTPUT FORMAT:


* Line 1: The correct value of N.


SAMPLE OUTPUT (file digits.out):


14


OUTPUT DETAILS:


The correct value of N is 14 ("1110" in base 2, "112" in base 3).

INPUT FORMAT:


* 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 FORMAT:


* Line 1: The correct value of N.

1010
212

14