Codeforces Round 283 (Div. 1) |
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Finished |

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E. Subsequences Return

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputAssume that *s*_{k}(*n*) equals the sum of digits of number *n* in the *k*-based notation. For example, *s*_{2}(5) = *s*_{2}(101_{2}) = 1 + 0 + 1 = 2, *s*_{3}(14) = *s*_{3}(112_{3}) = 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 10^{9} + 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*_{i1}, ..., *a*_{k} = *b*_{ik}. In particular, an empty sequence (i.e. the sequence consisting of zero elements) is a subsequence of any sequence.

Input

The first line contains two space-separated numbers *n* and *k* (1 ≤ *n* ≤ 10^{18}, 2 ≤ *k* ≤ 30).

Output

In a single line print the answer to the problem modulo 10^{9} + 7.

Examples

Input

4 2

Output

11

Input

7 7

Output

128

Note

In the first sample the sequence *a*_{i} looks as follows: (0, 1, 1, 0). All the possible subsequences are:

In the second sample the sequence *a*_{i} 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 2^{7} = 128 such sequences.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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