5391: Subsequences Return
内存限制：256 MB
时间限制：2 S
题面：传统
评测方式：文本比较
上传者：
提交：2
通过：1
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.
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.
输入样例 复制
输出样例 复制