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
import math

stdin = sys.stdin

ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
ns = lambda: stdin.readline().rstrip()  # ignore trailing spaces

n, k = na()
mod = 1000000007

s = int(math.sqrt(n))
dp = [1] * (n//s+1)
ep = [0] * s
dp[0] = 0

for i in range(1,s):
    ep[i] = 1 # n//i-n//(i+1)

for z in range(k-1):
    ndp = [0] * (n//s+1)
    nep = [0] * s

    for i in range(1,n//s+1):
        if i < s:
            nep[i] += dp[i]
        else:
            ndp[n//i] += dp[i]
    for i in range(1,s):
        ndp[i] += ep[i] * (n//i-n//(i+1))
        ndp[i] %= mod
    for i in range(2, s):
        nep[i] += nep[i-1]
        if nep[i] >= mod:
            nep[i] -= mod
    ndp[n//s] += nep[-1]
    ndp[n//s] %= mod
    for i in range(n//s-1, 0, -1):
        ndp[i] += ndp[i+1]
        if ndp[i] >= mod:
            ndp[i] -= mod
    dp, ep = ndp, nep

ans = sum(dp)
for i in range(1, s):
    ans += ep[i] * (n//i-n//(i+1))
print(ans%mod)