Problem:
Score : 600 points

Problem Statement

Find the number of sequences of length K consisting of positive integers such that the product of any two adjacent elements is at most N, modulo 10^9+7.

Constraints

1\leq N\leq 10^9

1 2\leq K\leq 100 (fixed at 21:33 JST)

N and K are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the number of sequences, modulo 10^9+7.

Sample Input 1

3 2

Sample Output 1

5

(1,1), (1,2), (1,3), (2,1), and (3,1) satisfy the condition.

Sample Input 2

10 3

Sample Output 2

147

Sample Input 3

314159265 35

Sample Output 3

457397712

Solution in JavaScript (node.js v5.12) (judge verdict: Accepted)

var GET=(function(){function f(s){return new g(s);}function g(s){this._s=s.trim().split("\n");this._y=0;}g.prototype.a=function(f){var s=this._s, y=this._y, r;if(typeof s[y]==="string")s[y]=s[y].split(" ").reverse();r=s[y].pop();if(!s[y].length)this._y++;return f?r:+r;};g.prototype.l=function(f){var s=this._s[this._y++].split(" ");return f?s:s.map(a=>+a);};g.prototype.m=function(n,f){var r=this._s.slice(this._y,this._y+=n).map(a=>a.split(" "));return f?r:r.map(a=>a.map(a=>+a));};g.prototype.r=function(n,f){var r=this._s.slice(this._y,this._y+=n);return f?r:r.map(a=>+a);};return f;})();
var o=GET(require("fs").readFileSync("/dev/stdin","utf8"));
function xArray(v){var a=arguments,l=a.length,r="Array(a["+--l+"]).fill(0).map(x=>{return "+v+";})";while(--l)r="Array(a["+l+"]).fill(0).map(x=>"+r+")";return eval(r);}
var mod=1e9+7;
function abmod(){for(var a=arguments,r=a[0],i=1;i<a.length;)r=((r>>16)*a[i]%mod*65536+(r&65535)*a[i++])%mod;return r;}

console.log(main());
function main(){
  var n=o.a();
  var k=o.a();
  var m=Math.sqrt(n)|0;
  var dp=xArray(0,k+1,m+1);
  var dp2=xArray(0,k+1,m+1);
  var a=Array(m+1);
  dp[0][1]=1;
  var x=n/m|0;
  a[m]=x-m;
  for(var i=m-1;i;i--){
    a[i]=(n/i|0)-x;
    x+=a[i];
  }
  for(var i=1;i<=k;i++){
    var x=0;
    for(var j=1;j<=m;j++){
      x+=dp[i-1][j];
      x%=mod;
      dp2[i][j]+=abmod(a[j],x);
      dp2[i][j]%=mod;
    }
    for(var j=m;j;j--){
      x+=dp2[i-1][j];
      x%=mod;
      dp[i][j]+=x;
      dp[i][j]%=mod;
    }
  }
  var ans=0;
  for(var i=1;i<=m;i++){
    ans+=dp[k][i]+dp2[k][i];
  }
  return ans%mod;
}