Beautiful Numbers
Time Limit:1000MS Memory Limit:65536K
Total Submit:298 Accepted:59
Description Now
that you believe Jiajia & Wind's cute daughter, Autumn, is a
genius. It's not surprising that such a clever little girl would have
no interest on simple additions very soon. This time, she turned to
divisions, since they're more fun. For example, she found herself that
if the sum of digits of a decimal number is a multiple of 3, then the
decimal number itself is also a multiple of 3. The argument is still
true if she replaces the number 3 with 9.
Inspired by these, Autumn invented a special kind of number, called
'Beautiful Numbers'. A number k is said to be Beautiful in base b, if
the sum of digits of k in base b is a multiple of b.
Autumn knows how to calculate the sum of first n beautiful numbers in base b, can you?
Input The input contains a single test case with two lines. The first line is a single integer n(n < 101001), the second line is a single integer b(1 < b < 1001).
Output The
output contains a single integer, the sum of first n beautiful numbers
in base b. You should output the sum in decimal, not in base b.
Sample Input
2
3
Sample Output
12
Source POJ Monthly--2006.02.26,zgl & twb
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