Mashmokh‘s boss, Bimokh, didn‘t like Mashmokh. So he fired him. Mashmokh decided to go to university and participate in ACM instead of finding a new job. He wants to become a member of Bamokh‘s team.
In order to join he was given some programming tasks and one week to solve them. Mashmokh is not a very experienced programmer. Actually he is not a programmer at all. So he wasn‘t able to solve them. That‘s why he asked you to help him with these tasks. One
of these tasks is the following.
A sequence of l integers b1,?b2,?...,?bl (1?≤?b1?≤?b2?≤?...?≤?bl?≤?n) is
called good if each number divides (without a remainder) by the next number in the sequence. More formally for
all i (1?≤?i?≤?l?-?1).
Given n and k find the number of good sequences of
length k. As the answer can be rather large print it modulo 1000000007 (109?+?7).
Input
The first line of input contains two space-separated integers n,?k (1?≤?n,?k?≤?2000).
Output
Output a single integer — the number of good sequences of length k modulo 1000000007 (109?+?7).
Sample test(s)
input
3 2
output
5
input
6 4
output
39
input
2 1
output
2
Note
In the first sample the good sequences are: [1,?1],?[2,?2],?[3,?3],?[1,?2],?[1,?3].
题目就是有关计数问题的DP;
设dp[i][j]表示以i为结尾长度为j的方案数:dp[i][j]=sum(dp[k][j-1])(i%k==0)
特别的dp[i][1]=1;
#include<cstdio> #include<cstring> #include<algorithm> #include<vector> #include<string> #include<iostream> #include<queue> #include<cmath> #include<map> #include<stack> #include<set> using namespace std; #define REPF( i , a , b ) for ( int i = a ; i <= b ; ++ i ) #define REP( i , n ) for ( int i = 0 ; i < n ; ++ i ) #define CLEAR( a , x ) memset ( a , x , sizeof a ) typedef long long LL; typedef pair<int,int>pil; const int INF = 0x3f3f3f3f; const int MOD=1e9+7; const int maxn=2000+100; LL dp[maxn][maxn]; int n,k; int main() { while(cin>>n>>k) { CLEAR(dp,0); REPF(i,1,n) dp[i][1]=1; for(int j=1;j<=n;j++) for(int kk=j;kk<=n;kk+=j) for(int i=2;i<=k;i++) dp[kk][i]=(dp[kk][i]+dp[j][i-1])%MOD; LL ans=0; REPF(i,1,n) ans=(ans+dp[i][k])%MOD; cout<<ans<<endl; } return 0; }