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 sys
def input():
	return sys.stdin.readline().strip()

N, K = list(map(int, input().split()))

rootN = int(N**0.5)
num_list = [1]*rootN

now = rootN
for num in range(rootN, 0, -1):
	x = N//num
	num_list.append(x - now)
	now = x

dp = [[0]*len(num_list) for i in range(K)]
for i in range(len(num_list)):
	dp[0][i] = num_list[i]


mod = 10**9 + 7
for k in range(1, K):
	sum_before = [dp[k - 1][0]]
	for i in range(1, len(num_list)):
		sum_before.append(sum_before[-1]+dp[k - 1][i])
	for i in range(len(num_list)):
		dp[k][i] = (num_list[i]*sum_before[len(num_list) - 1 - i])%mod

print(sum(dp[-1])%mod)