Buggy python submission (verdict: Time Limit Exceeded):
import sys

def solve():
    N, K = map(int, input().split())
    mod = 7 + 10 ** 9
    lim = 0
    for i in range(1, 10 ** 5):
        if i ** 2 > N:
            lim = i - 1
            break
    
    large = [0] * (lim + 1)
    for i in range(1, lim): large[i] = (N // i) - (N // (i + 1))
    large[lim] = N // lim - lim
   
    
    DP = [[0 for j in range(lim + 1)] for i in range(K)] #x <= lim
    DP[0] = [1] * (lim + 1)

    DPlarge = [[0 for j in range(lim + 1)] for i in range(K)] #x >= lim
    for i in range(1, lim+1): DPlarge[0][i] = large[i]

    for k in range(K-1):
        for i in range(1, lim + 1):
            for t in range(1, i + 1):
                DP[k+1][t] += DPlarge[k][i]
                DP[k+1][t] %= mod
                DP[k+1][t] += DP[k][i]
                DP[k+1][t] %= mod
            
            DPlarge[k+1][i] += (DP[k][i] * large[i]) % mod
            DPlarge[k+1][i] %= mod

            for t in range(i + 1, lim + 1):
                DPlarge[k+1][t] += (DP[k][i] * large[t]) % mod 
                DPlarge[k+1][t] %= mod
                DP[k+1][t] += DP[k][i]
                DP[k+1][t] %= mod
                

    ans = 0
    for i in range(1, lim+1):
        ans += (DP[K-1][i] + DPlarge[K-1][i]) % mod
        ans %= mod

    print(ans)
    #print(DP)
    #print(DPlarge)

    
    return 0

if __name__ == "__main__":
    solve()

Fixed submission:
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()

Buggy python submission (verdict: Time Limit Exceeded):
import sys

def solve():
    N, K = map(int, input().split())
    mod = 7 + 10 ** 9
    lim = 0
    for i in range(1, 10 ** 5):
        if i ** 2 > N:
            lim = i - 1
            break
    
    large = [0] * (lim + 1)
    for i in range(1, lim): large[i] = (N // i) - (N // (i + 1))
    large[lim] = N // lim - lim
   
    
    DP = [[0 for j in range(lim + 1)] for i in range(K)] #x <= lim
    DP[0] = [1] * (lim + 1)

    DPlarge = [[0 for j in range(lim + 1)] for i in range(K)] #x >= lim
    for i in range(1, lim+1): DPlarge[0][i] = large[i]

    for k in range(K-1):
        for i in range(1, lim + 1):
            for t in range(1, i + 1):
                DP[k+1][t] += DPlarge[k][i]
                DP[k+1][t] %= mod
                DP[k+1][t] += DP[k][i]
                DP[k+1][t] %= mod
            
            DPlarge[k+1][i] += (DP[k][i] * large[i]) % mod
            DPlarge[k+1][i] %= mod

            for t in range(i + 1, lim + 1):
                DPlarge[k+1][t] += (DP[k][i] * large[t]) % mod 
                DPlarge[k+1][t] %= mod
                DP[k+1][t] += DP[k][i]
                DP[k+1][t] %= mod
                

    ans = 0
    for i in range(1, lim+1):
        ans += (DP[K-1][i] + DPlarge[K-1][i]) % mod
        ans %= mod

    print(ans)
    #print(DP)
    #print(DPlarge)

    
    return 0

if __name__ == "__main__":
    solve()

Fixed submission:
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()