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#F1811. Subsequences Return

    ID: 1817 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 10 上传者: 标签>动态规划矩阵运算数学挑战难度共享题库Codeforces英文题面题目来源题面语言

Subsequences Return

题目描述

E. Subsequences Return
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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

Output

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

Examples
Input
4 2
Output
11
Input
7 7
Output
128
Note

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.

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 1371 题。保留原作者与原赛事署名。