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

input = lambda: sys.stdin.readline().rstrip()


def solve():

    S = input()
    S = S[::-1]
    MOD = 10 ** 9 + 7

    dp = [0] * 13
    dp[0] = 1

    mul = 1
    for i in range(len(S)):
        next_dp = [0] * 13
        if S[i] == '?':
            for k in range(10):
                for j in range(13):
                    jj = ((k * mul) + j) % 13
                    next_dp[jj] += dp[j]
                    next_dp[jj] %= MOD
        else:
            num = int(S[i])
            for j in range(13):
                jj = ((num * mul) + j) % 13
                next_dp[jj] += dp[j]
                next_dp[jj] %= MOD

        mul = mul * 10 % 13
        dp = next_dp

    print(dp[5])


if __name__ == '__main__':
    solve()


Fixed submission:
mod = 10 ** 9 + 7

S = input()
dp = [[0] * 13 for _ in range(len(S) + 1)]
dp[0][0] = 1
mul = 1

for i in range(len(S)):
    x = S[-(i + 1)]
    if x == "?":
        for k in range(10):
            for j in range(13):
                dp[i + 1][(mul * k + j) % 13] += dp[i][j]
                dp[i + 1][(mul * k + j) % 13] %= mod
    else:
        k = int(x)
        for j in range(13):
            dp[i + 1][(mul * k + j) % 13] += dp[i][j]
            dp[i + 1][(mul * k + j) % 13] %= mod
    mul = mul * 10 % 13

print(dp[len(S)][5])

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

input = lambda: sys.stdin.readline().rstrip()


def solve():

    S = input()
    S = S[::-1]
    MOD = 10 ** 9 + 7

    dp = [0] * 13
    dp[0] = 1

    mul = 1
    for i in range(len(S)):
        next_dp = [0] * 13
        if S[i] == '?':
            for k in range(10):
                for j in range(13):
                    jj = ((k * mul) + j) % 13
                    next_dp[jj] += dp[j]
                    next_dp[jj] %= MOD
        else:
            num = int(S[i])
            for j in range(13):
                jj = ((num * mul) + j) % 13
                next_dp[jj] += dp[j]
                next_dp[jj] %= MOD

        mul *= 10
        dp = next_dp

    print(dp[5])


if __name__ == '__main__':
    solve()


Fixed submission:
mod = 10 ** 9 + 7

S = input()
dp = [[0] * 13 for _ in range(len(S) + 1)]
dp[0][0] = 1
mul = 1

for i in range(len(S)):
    x = S[-(i + 1)]
    if x == "?":
        for k in range(10):
            for j in range(13):
                dp[i + 1][(mul * k + j) % 13] += dp[i][j]
                dp[i + 1][(mul * k + j) % 13] %= mod
    else:
        k = int(x)
        for j in range(13):
            dp[i + 1][(mul * k + j) % 13] += dp[i][j]
            dp[i + 1][(mul * k + j) % 13] %= mod
    mul = mul * 10 % 13

print(dp[len(S)][5])

Buggy python submission (verdict: Time Limit Exceeded):
mod = 10 ** 9 + 7

S = input()
dp = [[0] * 13 for _ in range(len(S) + 1)]
dp[0][0] = 1
mul = 1

for i in range(len(S)):
    x = S[-(i + 1)]
    if x == "?":
        for k in range(10):
            for j in range(13):
                dp[i + 1][(k * (10**i) + j) % 13] += dp[i][j]
                dp[i + 1][(k * (10**i) + j) % 13] %= mod
    else:
        k = int(x)
        for j in range(13):
            dp[i + 1][(k * (10**i) + j) % 13] += dp[i][j]
            dp[i + 1][(k * (10**i) + j) % 13] %= mod
    #mul = mul * 10 % 13

print(dp[len(S)][5])


Fixed submission:
mod = 10 ** 9 + 7

S = input()
dp = [[0] * 13 for _ in range(len(S) + 1)]
dp[0][0] = 1
mul = 1

for i in range(len(S)):
    x = S[-(i + 1)]
    if x == "?":
        for k in range(10):
            for j in range(13):
                dp[i + 1][(mul * k + j) % 13] += dp[i][j]
                dp[i + 1][(mul * k + j) % 13] %= mod
    else:
        k = int(x)
        for j in range(13):
            dp[i + 1][(mul * k + j) % 13] += dp[i][j]
            dp[i + 1][(mul * k + j) % 13] %= mod
    mul = mul * 10 % 13

print(dp[len(S)][5])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
input = lambda: sys.stdin.readline().rstrip()

mod = 10**9 + 7


def solve():

    S = ['0'] + list(reversed(input()))
    N = len(S) - 1
    dp = [[-1 for _ in range(13)] for _ in range(N + 1)]
    dp[0][0] = 1

    for i in range(1, N + 1):
        if S[i] == '?':
            for j in range(13):
                if dp[i - 1][j] != -1:
                    for k in range(10):
                        n = k * (10 ** (i - 1))
                        r = n % 13
                        jj = (j + r) % 13
                        if dp[i][jj] == -1:
                            dp[i][jj] = dp[i - 1][j]
                        else:
                            dp[i][jj] = (dp[i][jj] + dp[i - 1][j]) % mod

        else:
            for j in range(13):
                if dp[i - 1][j] != -1:
                    n = int(S[i]) * (10 ** (i - 1))
                    r = n % 13
                    jj = (j + r) % 13
                    dp[i][jj] = dp[i - 1][j]

    ans = dp[N][5] if dp[N][5] != -1 else 0
    print(ans)


if __name__ == '__main__':
    solve()


Fixed submission:
mod = 10 ** 9 + 7

S = input()
dp = [[0] * 13 for _ in range(len(S) + 1)]
dp[0][0] = 1
mul = 1

for i in range(len(S)):
    x = S[-(i + 1)]
    if x == "?":
        for k in range(10):
            for j in range(13):
                dp[i + 1][(mul * k + j) % 13] += dp[i][j]
                dp[i + 1][(mul * k + j) % 13] %= mod
    else:
        k = int(x)
        for j in range(13):
            dp[i + 1][(mul * k + j) % 13] += dp[i][j]
            dp[i + 1][(mul * k + j) % 13] %= mod
    mul = mul * 10 % 13

print(dp[len(S)][5])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
import numpy as np
input = lambda: sys.stdin.readline().rstrip()

mod = 10**9 + 7


def solve():

    S = ['0'] + list(reversed(input()))
    N = len(S) - 1
    dp = np.full((N + 1, 13), -1, dtype='i8')
    dp[0][0] = 1

    for i in range(1, N + 1):
        if S[i] == '?':
            for j in range(13):
                if dp[i - 1][j] != -1:
                    for k in range(10):
                        n = k * (10 ** (i - 1))
                        r = n % 13
                        jj = (j + r) % 13
                        if dp[i][jj] == -1:
                            dp[i][jj] = dp[i - 1][j]
                        else:
                            dp[i][jj] = (dp[i][jj] + dp[i - 1][j]) % mod

        else:
            for j in range(13):
                if dp[i - 1][j] != -1:
                    n = int(S[i]) * (10 ** (i - 1))
                    r = n % 13
                    jj = (j + r) % 13
                    dp[i][jj] = dp[i - 1][j]

    ans = dp[N][5] if dp[N][5] != -1 else 0
    print(ans)


if __name__ == '__main__':
    solve()


Fixed submission:
mod = 10 ** 9 + 7

S = input()
dp = [[0] * 13 for _ in range(len(S) + 1)]
dp[0][0] = 1
mul = 1

for i in range(len(S)):
    x = S[-(i + 1)]
    if x == "?":
        for k in range(10):
            for j in range(13):
                dp[i + 1][(mul * k + j) % 13] += dp[i][j]
                dp[i + 1][(mul * k + j) % 13] %= mod
    else:
        k = int(x)
        for j in range(13):
            dp[i + 1][(mul * k + j) % 13] += dp[i][j]
            dp[i + 1][(mul * k + j) % 13] %= mod
    mul = mul * 10 % 13

print(dp[len(S)][5])