Assume that s k (n) equals the sum of digits of number n in the k -based notation. For example, s 2(5) = s 2(1012) = 1 + 0 + 1 = 2, s 3(14) = s 3(1123) = 1 + 1 + 2 = 4. The sequence of integers a 0, ..., a n - 1 is defined as . Your task is to calculate the number of distinct subsequences of sequence a 0, ..., a n - 1 . Calculate the answer modulo 109 + 7. Sequence a 1, ..., a k is called to be a subsequence of sequence b 1, ..., b l , if there is a sequence of indices 1 ≤ i 1 i k ≤ l , such that a 1 = b i 1 , ..., a k = b i k . In particular, an empty sequence (i.e. the sequence consisting of zero elements) is a subsequence of any sequence.

输入描述:

The first line contains two space-separated numbers n and k (1 ≤ n ≤ 1018, 2 ≤ k ≤ 30).

输出描述:

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

备注:

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.