Buggy python submission (verdict: Time Limit Exceeded):
S = input()
ans = [[0] * 13 for _ in range(len(S))]
MOD = 10 ** 9 + 7
if S[0] == "?":
    for i in range(10):
        ans[0][i] = 1
else:
    ans[0][int(S[0])] = 1

for i, s in enumerate(S):
    if i == 0:
        continue
    if s == "?":
        for n in range(10):
            for j in range(13):
                ans[i][(j * 10 + n) % 13] += ans[i - 1][j]
                ans[i][(j * 10 + n) % 13] %= MOD
    else:
        for j in range(13):
            ans[i][(j * 10 + int(s)) % 13] = ans[i - 1][j]

print(ans[-1][5])


Fixed submission:
S = input()
ans = [[0] * 13 for _ in range(len(S))]
MOD = 10 ** 9 + 7
if S[0] == "?":
    for i in range(10):
        ans[0][i] = 1
else:
    ans[0][int(S[0])] = 1

for i, s in enumerate(S):
    if i == 0:
        continue
    if s == "?":
        for n in range(10):
            for j in range(13):
                ans[i][(j * 10 + n) % 13] += ans[i - 1][j]
                ans[i][(j * 10 + n) % 13] %= MOD
    else:
        for j in range(13):
            ans[i][(j * 10 + int(s)) % 13] = ans[i - 1][j]

print(ans[-1][5])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
S = S[::-1]
ans = [[0] * 13 for _ in range(len(S))]
MOD = 10 ** 9 + 7
if S[0] == "?":
    for i in range(10):
        ans[0][i] = 1
else:
    ans[0][int(S[0])] = 1

for i, s in enumerate(S):
    base = 10 ** i
    if i == 0:
        continue
    if s == "?":
        for n in range(10):
            for j in range(13):
                ans[i][(j + n * base) % 13] += ans[i - 1][j]
                ans[i][(j + n * base) % 13] %= MOD
    else:
        for j in range(13):
            ans[i][(j + int(s) * base) % 13] = ans[i - 1][j]

print(ans[-1][5])


Fixed submission:
S = input()
ans = [[0] * 13 for _ in range(len(S))]
MOD = 10 ** 9 + 7
if S[0] == "?":
    for i in range(10):
        ans[0][i] = 1
else:
    ans[0][int(S[0])] = 1

for i, s in enumerate(S):
    if i == 0:
        continue
    if s == "?":
        for n in range(10):
            for j in range(13):
                ans[i][(j * 10 + n) % 13] += ans[i - 1][j]
                ans[i][(j * 10 + n) % 13] %= MOD
    else:
        for j in range(13):
            ans[i][(j * 10 + int(s)) % 13] = ans[i - 1][j]

print(ans[-1][5])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
S = S[::-1]
ans = [[0] * 13 for _ in range(len(S))]
MOD = 10 ** 9 + 7
if S[0] == "?":
    for i in range(10):
        ans[0][i] = 1
else:
    ans[0][int(S[0])] = 1

for i, s in enumerate(S):
    if i == 0:
        continue
    if s == "?":
        for n in range(10):
            for j in range(13):
                if ans[i - 1][j] == 0:
                    continue
                ans[i][(j + n * 10 ** i) % 13] += ans[i - 1][j]
                ans[i][(j + n * 10 ** i) % 13] %= MOD
    else:
        for j in range(13):
            ans[i][(j + int(s) * 10 ** i) % 13] = ans[i - 1][j]

print(ans[-1][5])


Fixed submission:
S = input()
ans = [[0] * 13 for _ in range(len(S))]
MOD = 10 ** 9 + 7
if S[0] == "?":
    for i in range(10):
        ans[0][i] = 1
else:
    ans[0][int(S[0])] = 1

for i, s in enumerate(S):
    if i == 0:
        continue
    if s == "?":
        for n in range(10):
            for j in range(13):
                ans[i][(j * 10 + n) % 13] += ans[i - 1][j]
                ans[i][(j * 10 + n) % 13] %= MOD
    else:
        for j in range(13):
            ans[i][(j * 10 + int(s)) % 13] = ans[i - 1][j]

print(ans[-1][5])