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:
import math
printn = lambda x: sys.stdout.write(x)
inn = lambda : int(input())
inl   = lambda: list(map(int, input().split()))
inm   = lambda:      map(int, input().split())
DBG = True  and False
def ddprint(x):
  if DBG:
    print(x)

R = 10**9+7
n,k = inm()
q = int(math.sqrt(n))
a = [ [0]*(q+1) for j in range(k) ]
b = [ [0]*(q+1) for j in range(k) ]
c = [0]*(q+1)
c[1] = n - n//2
for i in range(2,q):
    c[i] = n//i - n//(i+1)
c[q] = n//q - q
for i in range(1,q+1):
    a[0][i] = 1
    b[0][i] = c[i]


for j in range(1,k):
    aacc = [0]*(q+2)
    bacc = [0]*(q+2)
    for i in range(1,q+1):
        aacc[i] = (aacc[i-1] + a[j-1][i])%R
    for i in range(q,0,-1):
        bacc[i] = (bacc[i+1] + b[j-1][i])%R
    for i in range(1,q+1):
        a[j][i] = (aacc[q]+bacc[i])%R
        b[j][i] = (aacc[i]*c[i])%R

print( (sum(a[k-1]) + sum(b[k-1])) % R )