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:
from bisect import bisect_left
from math import sqrt
MOD = 10**9 + 7

def main():
    lim, n = map(int, input().split())
    num, tmp = [], []
    for i in range(1, int(sqrt(lim))+1):
        num.append(i)
        if i**2 != lim:
            tmp.append(lim//i)
    while len(tmp) > 0:
        num.append(tmp.pop(-1))
    m = len(num)
    dp = [[0]*m for _ in range(n)]
    dp[0][0] = 1
    for j in range(1, m):
        dp[0][j] = num[j] - num[j-1]
    for i in range(1, n):
        for j in range(1, m):
            dp[i-1][j] += dp[i-1][j-1]
        for j in range(m):
            idx = bisect_left(num, lim//num[j])
            p = num[j]
            if j > 0:
                p -= num[j-1]
            dp[i][j] = dp[i-1][idx] * p % MOD
    print(sum(dp[-1])%MOD)

if __name__ == "__main__":
    main()