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 \le i1 \lt ... \lt ik \le 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 \le n \le 1018, 2 \le k \le 30).

In a single line print the answer to the problem modulo 109+7.

In the first sample the sequence ai looks as follows: (0,1,1,0). All the possible subsequences are:
(),(0),(0,0),(0,1),(0,1,0),(0,1,1),(0,1,1,0),(1),(1,0),(1,1),(1,1,0).
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.