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:
# Nが100以下の時は全部れっきょ

import math
N, K = map(int, input().split())
mod = 10**9+7


def rev(X):
    return pow(X, mod-2, mod)


if N <= 100:
    dp = [[0 for i in range(N+2)] for i in range(K+1)]
    for i in range(1, N+1):
        dp[1][i] += 1
    for i in range(2, K+1):
        for j in range(1, N+1):
            dp[i][1] += dp[i-1][j]
            dp[i][N//j+1] -= dp[i-1][j]
        for j in range(1, N+2):
            dp[i][j] += dp[i][j-1]
    ans = 0
    for i in range(1, N+1):
        ans += dp[K][i]
    print(ans % mod)
    exit()


else:
    # N>100
    ans = 0
    L=0
    for i in range(10**5):
        if i**2>N:
            L=i  
            break
    B = N//L
    dp = [[0 for i in range(L+B)] for i in range(K+1)]
    cnt = [0 for i in range(L+B)]
    for i in range(1, B+1):
        dp[1][i] += 1
        cnt[i] = 1
    for i in range(B+1, B+L):
        x = B+L-i
        dp[1][i] += N//x-N//(x+1)
        cnt[i] = N//x-N//(x+1)
    for i in range(2, K+1):
        S = sum(dp[i-1])
        for j in range(1, L+B-1):
            dp[i][j] = S*cnt[j] % mod
            S -= dp[i-1][-j]
        dp[i][L+B-1] = S*cnt[L+B-1] % mod
    for i in range(1, L+B):
        ans += dp[K][i]
        ans %= mod
    print(ans)