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:
n,k = map(int, input().split())
mod = 10**9 + 7

nums = set()
d = {}
for i in range(1,10**6):
    a = n//i
    b = 1 + n//(i+1)
    d[i] = a
    nums.add(i)
    nums.add(a)
    if(i >= b):
        break
    d[b] = i
    nums.add(b)

d = sorted(d.items())

dic_en = {}
dic_de = {}
nums = sorted(list(nums))
cnt = [0] * len(nums)
done = 0
for i,num in enumerate(nums):
    dic_en[num] = i
    dic_de[i] = num
    cnt[i] = num - done
    done = num

d = []
for num in nums:
    d.append((dic_en[num],  dic_en[n//num]))

op = cnt[::]

def update(op):
    n = len(nums)
    res = [0] * (n+1)
    for a,b in d:
        res[0] += op[a]
        res[b+1] -= op[a]
    res[0] %= mod
    for i in range(1,n):
        res[i] += res[i-1]
        res[i] %= mod
    for i in range(n):
        res[i] *= cnt[i]
        res[i] %= mod
    return res[:-1]

for i in range(k-1):
    op = update(op)

ans = sum(op) % mod

print(ans)