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 solve():
    input = sys.stdin.readline
    N, K = map(int, input().split())
    mod = 7 + 10 ** 9
    S = 1
    while S ** 2 <= N:
        S += 1
    DP = [[[0, 0] for _ in range(S)] for _ in range(K)]
    Rev = [0] * S
    S -= 1
    Rev[S] = (N // S - S) % mod
    for i in reversed(range(1, S)):
        Rev[i] = ((N // i) - (N // (i + 1))) % mod
    for i in range(1, S + 1):
        DP[0][i][0] = 1
        DP[0][i][1] = Rev[i]
    for i in range(2, S + 1):
        DP[0][i][0] += DP[0][i-1][0]
        DP[0][i][0] %= mod
    DP[0][S][1] += DP[0][S][0]
    DP[0][S][1] %= mod
    for i in reversed(range(1, S)):
        DP[0][i][1] += DP[0][i+1][1]
        DP[0][i][1] %= mod

    for i in range(1, K):
        for j in range(1, S + 1):
            DP[i][j][0] += DP[i-1][j][1]
            DP[i][j][1] += (DP[i-1][j][0] * Rev[j]) % mod
            DP[i][j][1] %= mod
            DP[i][j][0] += DP[i][j-1][0]
            DP[i][j][0] %= mod
        DP[i][S][1] += DP[i][S][0]
        DP[i][S][1] %= mod
        for j in reversed(range(1, S)):
            DP[i][j][1] += DP[i][j+1][1]
            DP[i][j][1] %= mod

    print(DP[K-1][1][1])
    #print(DP)

    return 0

if __name__ == "__main__":
    solve()