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 <bits/stdc++.h>
using namespace std;
using lint = long long int;
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)

constexpr int MOD = 1000000007;

int main()
{
    int N, K;
    cin >> N >> K;
    vector<int> vp;
    for (int i = 1; i * i <= N; i++)
    {
        vp.emplace_back(i);
        if (i != N / i) vp.emplace_back(N / i);
    }
    sort(vp.begin(), vp.end());
    REP(i, vp.size() - 1) vp[i] = vp[i + 1] - vp[i];
    vector<int> dp(vp.size());
    dp[0] = 1;
    REP(_, K)
    {
        reverse(dp.begin(), dp.end());
        IREP(i, dp.size() - 1)
        {
            (dp[i] += dp[i + 1]) %= MOD;
            dp[i + 1] = dp[i + 1] * (lint)vp[i] % MOD;
        }
    }
    cout << accumulate(dp.begin(), dp.end(), 0LL) % MOD << endl;
}