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 PYTHON3):

Solution:
# coding: utf-8
# Your code here!
MOD = 10**9+7

from math import sqrt, floor

n,k = [int(i) for i in input().split()]
sn = floor(sqrt(n))+1

pre = [0]*sn
pre[1] = 1

cur = [1]*(sn)
cur[0] = 0

#big = n-sn+1

for _ in range(k-1):
#    print(cur)
    new = [sum(cur)%MOD]*(sn); new[0] = 0
    s = sum(pre)%MOD
    b=0
    res=0
    for j in range(sn-1,0,-1):
        a = n//j - (sn-1) #okな個数
        res += (a-b)*s
        res %=MOD
        new[j] += res
        if new[j] > MOD: new[j] -= MOD
        s -= pre[j]
        b=a
        
    pre,cur = cur,new


#print(pre,cur)
ans =0
for j in range(sn-1,0,-1):
    ans += pre[j]*(n//j - (sn-1))
    ans %=MOD


print((sum(cur)+ans)%MOD)