Problem: 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.

Examples

Input

3 2


Output

5


Input

10 3


Output

147


Input

314159265 35


Output

457397712

Solution (in CPP):

Solution:
#include <stdio.h>
#include <math.h>
#define mod 1000000007
using namespace std;
typedef long long ll;

int main(void) {
  ll i, j, k, n, m, t;
  scanf("%lld%lld", &n, &k);
  t = sqrt(n);
  m = t * 2;
  if(t * (t + 1) > n) m--;
  ll dp[k][m], cnt[m], sum;
  for(i = 1; i <= t; ++i) {
    cnt[i - 1] = 1;
    cnt[m - i] = n / i - n / (i + 1);
  }
  for(i = 0; i < m; ++i) dp[0][i] = 1;
  for(i = 1; i < k; ++i) {
    sum = dp[i - 1][0];
    dp[i][m - 1] = sum;
    for(j = 1; j < m; ++j) {
      sum += dp[i - 1][j] * cnt[j];
      sum %= mod;
      dp[i][m - 1 - j] = sum;
    }
  }
  sum = 0;
  for(i = 0; i < m; ++i) sum += dp[k - 1][i] * cnt[i], sum %= mod;
  printf("%lld", sum);
  return 0;
}