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, K = map(int, input().split())
MOD = 10**9 + 7

sq = 0
while (sq + 1) * (sq + 1) <= N:
    sq += 1

num = [0 for i in range(2 * sq + 1)]
for i in range(1, sq + 1):
    num[i] = 1
for i in range(1, sq + 1):
    lo = max(sq + 1, (N + i + 1) // (i + 1))
    hi = N // i
    num[2 * sq + 1 - i] = hi - lo + 1

dp = [[0 for j in range(2 * sq + 2)] for i in range(K + 1)]
dp[0][1] = 1
for i in range(K):
    for j in range(1, 2 * sq + 1):
        ways = dp[i][j] * num[j] % MOD
        dp[i + 1][1] += ways
        dp[i + 1][2 * sq + 2 - j] -= ways
    for j in range(1, 2 * sq + 1):
        dp[i + 1][j] += dp[i + 1][j - 1]

ans = 0
for j in range(1, 2 * sq + 1):
    ans += dp[K][j] * num[j]
print(ans % MOD)