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).
The first line of input contains two space-separated integers n, k (1 ≤ n, k ≤ 2000).
Output a single integer — the number of good sequences of length k modulo 1000000007 (109 + 7).
3 2
5
In the first sample the good sequences are: [1, 1], [2, 2], [3, 3], [1, 2], [1, 3].
题意:给你一个N,K, 表示从1到n,选取长度为k的序列A满足 Ai整除Ai-1
题解:dp[i][j]表示长度为j是最大为i的序列方案数
//1085422276 #include<iostream> #include<cstdio> #include<cstring> #include<string> #include<algorithm> #include<queue> #include<cmath> #include<map> #include<bitset> #include<set> #include<vector> using namespace std ; typedef long long ll; #define mem(a) memset(a,0,sizeof(a)) #define meminf(a) memset(a,127,sizeof(a)); #define memfy(a) memset(a,-1,sizeof(a)) #define TS printf("111111 "); #define FOR(i,a,b) for( int i=a;i<=b;i++) #define FORJ(i,a,b) for(int i=a;i>=b;i--) #define READ(a,b,c) scanf("%d%d%d",&a,&b,&c) #define mod 1000000007 #define maxn 2005 inline ll read() { ll x=0,f=1; char ch=getchar(); while(ch<'0'||ch>'9') { if(ch=='-')f=-1; ch=getchar(); } while(ch>='0'&&ch<='9') { x=x*10+ch-'0'; ch=getchar(); } return x*f; } //**************************************** ll dp[maxn][maxn]; int main() { int n=read(),m=read(); mem(dp); FOR(i,1,n)dp[i][1]=1; FOR(k,1,m-1) FOR(i,1,n) { if(dp[i][k]) for(int j=i;j<=n;j+=i) { dp[j][k+1]=(dp[j][k+1]+dp[i][k])%mod; } } ll ans=0; FOR(i,1,n)ans=(ans+dp[i][m])%mod; cout<<ans<<endl; return 0; }