Buggy python submission (verdict: Runtime Error):
N = int(input())
K = int(input())
L = len(str(N))

def solve(num_str, k, smaller):
    if k == 0 or num_str == None:
        return 1

    elif smaller:
        keta = len(num_str)
        if k == 1:
            return keta * 9
        elif k == 2:
            return keta * (keta-1)//2 * 9 * 9
        else:
            return keta * (keta-1) * (keta -2)//6 * 9 * 9 * 9
    else:   
        num = int(num_str)
        num_str = str(num_str)
        top = int(num_str[0])
        if top:
            zero = solve(num_str[1:], k, True)
            non_zero = solve(num_str[1:], k-1, True) * (top - 1)
            just = solve(num_str[1:], k-1, False)
            return zero + non_zero + just
        else:
            return solve(num_str[1:], k, False)
print(solve(str(N), K, False))

Fixed submission:
N = int(input())
K = int(input())
L = len(str(N))

suu = []
for i in range(L):
    suu.append(int(str(N)[i]))

DP_1 =[[0 for k in range(L+2)] for i in range(L+1)]
DP_2 =[[0 for k in range(L+2)] for i in range(L+1)]
DP_2[0][0] = 1
for i in range(L):
    for k in range(L+1):
        DP_1[i+1][k] = DP_1[i][k] + DP_1[i][k-1] * 9 
        if suu[i]:
            DP_1[i+1][k] += DP_2[i][k] + DP_2[i][k-1] * max(suu[i] - 1, 0)
            DP_2[i+1][k] = DP_2[i][k-1]
        else:
            DP_2[i+1][k] = DP_2[i][k]
print(DP_1[L][K]+ DP_2[L][K])

Buggy python submission (verdict: Runtime Error):
N = int(input())
K = int(input())
L = len(str(N))

def solve(num_str, k, smaller):

    keta = len(num_str)
    if k == 0:
        return 1
    elif smaller:
        if k == 1:
            return keta * 9
        elif k == 2:
            return keta * (keta-1)//2 * 9 * 9
        else:
            return keta * (keta-1) * (keta -2)//6 * 9 * 9 * 9
    else:   
        num = int(num_str)
        num_str = str(num_str)
        top = int(num_str[0])
        if top:
            zero = solve(num_str[1:], k, True)
            non_zero = solve(num_str[1:], k-1, True) * (top - 1)
            just = solve(num_str[1:], k-1, False)
            return zero + non_zero + just
        else:
            return solve(num_str[1:], k, False)
print(solve(str(N), K, False))

Fixed submission:
N = int(input())
K = int(input())
L = len(str(N))

suu = []
for i in range(L):
    suu.append(int(str(N)[i]))

DP_1 =[[0 for k in range(L+2)] for i in range(L+1)]
DP_2 =[[0 for k in range(L+2)] for i in range(L+1)]
DP_2[0][0] = 1
for i in range(L):
    for k in range(L+1):
        DP_1[i+1][k] = DP_1[i][k] + DP_1[i][k-1] * 9 
        if suu[i]:
            DP_1[i+1][k] += DP_2[i][k] + DP_2[i][k-1] * max(suu[i] - 1, 0)
            DP_2[i+1][k] = DP_2[i][k-1]
        else:
            DP_2[i+1][k] = DP_2[i][k]
print(DP_1[L][K]+ DP_2[L][K])

Buggy python submission (verdict: Runtime Error):
N = int(input())
K = int(input())
L = len(str(N))

suu = []
for i in range(L):
    suu.append(int(str(N)[i]))

DP_1 =[[0 for k in range(L+1)] for i in range(L+2)]
DP_2 =[[0 for k in range(L+1)] for i in range(L+2)]
DP_2[0][0] = 1
for i in range(L):
    for k in range(L+1):
        DP_1[i+1][k] = DP_1[i][k] + DP_1[i][k-1] * 9 
        if suu[i]:
            DP_1[i+1][k] += DP_2[i][k] + DP_2[i][k-1] * max(suu[i] - 1, 0)
            DP_2[i+1][k] = DP_2[i][k-1]
        else:
            DP_2[i+1][k] = DP_2[i][k]
print(DP_1[L][K]+ DP_2[L][K])

Fixed submission:
N = int(input())
K = int(input())
L = len(str(N))

suu = []
for i in range(L):
    suu.append(int(str(N)[i]))

DP_1 =[[0 for k in range(L+2)] for i in range(L+1)]
DP_2 =[[0 for k in range(L+2)] for i in range(L+1)]
DP_2[0][0] = 1
for i in range(L):
    for k in range(L+1):
        DP_1[i+1][k] = DP_1[i][k] + DP_1[i][k-1] * 9 
        if suu[i]:
            DP_1[i+1][k] += DP_2[i][k] + DP_2[i][k-1] * max(suu[i] - 1, 0)
            DP_2[i+1][k] = DP_2[i][k-1]
        else:
            DP_2[i+1][k] = DP_2[i][k]
print(DP_1[L][K]+ DP_2[L][K])

Buggy python submission (verdict: Runtime Error):
N = int(input())
K = int(input())
L = len(str(N))

suu = []
for i in range(L):
    suu.append(int(str(N)[i]))

DP_1 =[[0 for k in range(L+1)] for i in range(L+1)]
DP_2 =[[0 for k in range(L+1)] for i in range(L+1)]
DP_2[0][0] = 1
for i in range(L):
    for k in range(L+1):
        DP_1[i+1][k] = DP_1[i][k] + DP_1[i][k-1] * 9 
        if suu[i]:
            DP_1[i+1][k] += DP_2[i][k] + DP_2[i][k-1] * max(suu[i] - 1, 0)
            DP_2[i+1][k] = DP_2[i][k-1]
        else:
            DP_2[i+1][k] = DP_2[i][k]
print(DP_1[L][K]+ DP_2[L][K])

Fixed submission:
N = int(input())
K = int(input())
L = len(str(N))

suu = []
for i in range(L):
    suu.append(int(str(N)[i]))

DP_1 =[[0 for k in range(L+2)] for i in range(L+1)]
DP_2 =[[0 for k in range(L+2)] for i in range(L+1)]
DP_2[0][0] = 1
for i in range(L):
    for k in range(L+1):
        DP_1[i+1][k] = DP_1[i][k] + DP_1[i][k-1] * 9 
        if suu[i]:
            DP_1[i+1][k] += DP_2[i][k] + DP_2[i][k-1] * max(suu[i] - 1, 0)
            DP_2[i+1][k] = DP_2[i][k-1]
        else:
            DP_2[i+1][k] = DP_2[i][k]
print(DP_1[L][K]+ DP_2[L][K])

Buggy python submission (verdict: Runtime Error):
N = int(input())
K = int(input())
L = len(str(N))

suu = []
for i in range(L):
    suu.append(int(str(N)[i]))

DP_1 =[[0 for k in range(L+1)] for i in range(L+1)]
DP_2 =[[0 for k in range(L+1)] for i in range(L+1)]
DP_2[0][0] = 1
for i in range(L):
    for k in range(L+1):
        DP_1[i+1][k] = DP_1[i][k] + DP_1[i][k-1] * 9 
        if suu[i]:
            DP_1[i+1][k] += DP_2[i][k] + DP_2[i][k-1] * max(suu[i] - 1, 0)
            DP_2[i+1][k] = DP_2[i][k-1]
        else:
            DP_2[i+1][k] = DP_2[i][k]
print(DP_1[L][K]+ DP_2[L][K])

Fixed submission:
N = int(input())
K = int(input())
L = len(str(N))

suu = []
for i in range(L):
    suu.append(int(str(N)[i]))

DP_1 =[[0 for k in range(L+2)] for i in range(L+1)]
DP_2 =[[0 for k in range(L+2)] for i in range(L+1)]
DP_2[0][0] = 1
for i in range(L):
    for k in range(L+1):
        DP_1[i+1][k] = DP_1[i][k] + DP_1[i][k-1] * 9 
        if suu[i]:
            DP_1[i+1][k] += DP_2[i][k] + DP_2[i][k-1] * max(suu[i] - 1, 0)
            DP_2[i+1][k] = DP_2[i][k-1]
        else:
            DP_2[i+1][k] = DP_2[i][k]
print(DP_1[L][K]+ DP_2[L][K])