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

MOD = 10**9 + 7


def main():
    N, K = map(int, input().split())
    R = int(math.sqrt(N))
    if N // R == R:
        M = R * 2 - 1
    else:
        M = R * 2
    mapping = [0] * (M+1)
    for i in range(1, R+1):
        mapping[i] = i
        mapping[-i] = N//i
    cnt = [0] * (M+1)
    for i in range(1, M+1):
        cnt[i] = mapping[i] - mapping[i-1]
    dp = [[0] * (M+1) for _ in range(K+1)]
    dp[0] = list(cnt)
    for i in range(M):
        dp[0][i+1] += dp[0][i]

    for i in range(K-1):
        for j in range(1, M+1):
            if j <= R:
                idx = -j
            else:
                idx = M - j + 1
            dp[i+1][j] = dp[i][idx]
        for j in range(M):
            dp[i+1][j+1] = (dp[i+1][j] + dp[i+1][j+1] * cnt[j+1]) % MOD
    print(dp[K-1][M])


if __name__ == "__main__":
    main()