1928: Decimal integer conversion

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XiaoMing likes mathematics, and he is just learning how to convert numbers between different
bases , but he keeps making errors since he is only 6 years old. Whenever XiaoMing converts a
number to a new base and writes down the result, he always writes one of the digits wrong.
For example , if he converts the number 14 into binary (i.e., base 2), the correct result should be
"1110", but he might instead write down "0110" or "1111". XiaoMing never accidentally adds or
deletes digits, so he might write down a number with a leading digit of " 0" if this is the digit she
gets wrong.
Given XiaoMing 's output when converting a number N into base 2 and base 3, please determine
the correct original value of N (in base 10). (N<=10^10)
You can assume N is at most 1 billion, and that there is a unique solution for N.

The first line of the input contains one integers T, which is the nember of test cases (1<=T<=8)
Each test case specifies:
* 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.

For each test case generate a single line containing a single integer ,  the correct value of N

1
1010
212


14