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 1995 Regional problem set
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Problem A  Long Multiplication  Filename LONGMULT
In traditional "long multiplication" we determine the product
of two integers, x and y, by multiplying x and the individual digits of
y, in turn, starting with the units digit. The results of these
multiplications are arranged appropriately and added, yielding the
completed product. The representation of these operations is
usually done in a particular manner. Consider the multiplication of
123 by 95: 123
95

615
1107

11685
The numbers to be multiplied, x and y, are each displayed on a
separate line, followed by a horizontal line. The results of
multiplying each digit of y by x are then displayed on separate lines,
followed by another horizontal line, and then the final product. In
this problem you are to perform a sequence of such multiplications,
displaying the results in this traditional representation.
Input
Each line of the input data, except the last, will contain two
integers, x and y, separated by whitespace (one or more blanks and tab
characters). Whitespace may also precede the first integer and follow
the second integer. Each integer will have no more than 10 digits. The
last line of the input data will contain only whitespace, and marks the
end of the input.
Output
For each pair of integers (that is, each input line except the
last), perform the multiplication of x by y, displaying the results in
the form shown above and in the examples shown below. Follow the
output for each multiplication by a blank line. If y contains only a
single significant digit, omit the second horizontal line and the sum
(since in that case it would be superfluous). Display 0 digits only
when they are significant.
The number of hyphens in the first horizontal line should be the
same as the number of digits in the larger of x and y. The number of
hyphens in the second horizontal line, if it is produced, should be the
same as the number of digits in the product of x and y.
Example Input
4 7
135 46
12345 862
this line is blank
Expected Output
4
7

28
135
46

810
540

6210
12345
862

24690
74070
98760

10641390
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Ed Karrels.
Last updated September 20, 1999