Long Multiplication -- Filename LONGMULT
Time Limit: 1000 ms Memory Limit: 65536 KiB
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.
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.
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.
4 7 135 46 12345 862 this line is blank
4 7 - 28 135 46 --- 810 540 ---- 6210 12345 862 ----- 24690 74070 98760 -------- 10641390