Instructions
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In positional notation we know the position of a digit indicates the weight of that digit toward the
value of a number. For example, in the base 10 number 362 we know that 2 has the weight 100, 6
has the weight 101, and 3 has the weight 102, yielding the value 3×102+ 6 ×101+ 2 ×100, or just
300 + 60 + 2. The same mechanism is used for numbers expressed in other bases. While most people
assume the numbers they encounter everyday are expressed using base 10, we know that other bases
are possible. In particular, the number 362 in base 9 or base 14 represents a totally dierent value than
362 in base 10.
For this problem your program will presented with a sequence of pairs of integers. Let’s call the
members of a pair Xand Y. What your program is to do is determine the smallest base for Xand the
smallest base for Y(likely dierent from that for X) so that Xand Yrepresent the same value.
Consider, for example, the integers 12 and 5. Certainly these are not equal if base 10 is used for
each. But suppose 12 was a base 3 number and 5 was a base 6 number? 12 base 3 = 1×31+ 2 ×30,
or 5 base 10, and certainly 5 in any base is equal to 5 base 10. So 12 and 5 can be equal, if you select
the right bases for each of them!
Input
On each line of the input data there will be a pair of integers, Xand Y, separated by one or more blanks;
leading and trailing blanks may also appear on each line, are are to be ignored. The bases associated
with Xand Ywill be between 1 and 36 (inclusive), and as noted above, need not be the same for Xand
Y. In representing these numbers the digits 0 through 9 have their usual decimal interpretations. The
uppercase alphabetic characters Athrough Zrepresent digits with values 10 through 35, respectively.
Output
For each pair of integers in the input display a message similar to those shown in the examples shown
below. Of course if the two integers cannot be equal regardless of the assumed base for each, then print
an appropriate message; a suitable illustration is given in the examples.
Sample Input
12 5
10 A
12 34
123 456
1 2
10 2
Sample Output
12 (base 3) = 5 (base 6)
10 (base 10) = A (base 11)
12 (base 17) = 34 (base 5)
123 is not equal to 456 in any base 2..36
1 is not equal to 2 in any base 2..36
10 (base 2) = 2 (base 3)
