2570: Subsequences Return
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
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Description
Assume that sk(n) equals the sum of digits of number n in the k-based notation. For example, s2(5)=s2(1012)=1+0+1=2, s3(14)=s3(1123)=1+1+2=4.
The sequence of integers a0,...,an-1 is defined as 
. Your task is to calculate the number of distinct subsequences of sequence a0,...,an-1. Calculate the answer modulo 109+7.
Sequence a1,...,ak is called to be a subsequence of sequence b1,...,bl, if there is a sequence of indices 1≤i1<...<ik≤l, such that a1=bi1, ..., ak=bik. In particular, an empty sequence (i.e. the sequence consisting of zero elements) is a subsequence of any sequence.
The first line contains two space-separated numbers n and k (1≤n≤1018, 2≤k≤30).
In a single line print the answer to the problem modulo 109+7.
4 2
11
7 7
128
In the first sample the sequence ai looks as follows: (0,1,1,0). All the possible subsequences are:
In the second sample the sequence ai looks as follows: (0,1,2,3,4,5,6). The subsequences of this sequence are exactly all increasing sequences formed from numbers from 0 to 6. It is easy to see that there are 27=128 such sequences.