Buggy python submission (verdict: Time Limit Exceeded):
s = input().strip()

DIV = 10**9 + 7
new = list(range(13))
old = None

c = s[-1]
if c == '?':
    old = [int(t < 10) for t in range(13)]
else:
    c = int(c)
    old = [int(t == c) for t in range(13)]

digit = 10
for i, c in enumerate(reversed(s[:-1])):
    for j in range(13):
        new[j] = 0
    if c == '?':
        for m in range(10):
            for mod, cnt in enumerate(old):
                shifted = (mod + m * digit) % 13
                new[shifted] += cnt
    else:
        c = int(c)
        for mod, cnt in enumerate(old):
            shifted = (mod + c * digit) % 13
            new[shifted] += cnt
    for j in range(13):
        new[j] %= DIV
    new, old = old, new
    digit = (digit * 10) % 13

print(old[5])

Fixed submission:
s = input().strip()

DIV = 10**9 + 7
new = list(range(13))
old = None

c = s[-1]
if c == '?':
    old = [int(t < 10) for t in range(13)]
else:
    c = int(c)
    old = [int(t == c) for t in range(13)]

digit = 10
for i, c in enumerate(reversed(s[:-1])):
    for j in range(13):
        new[j] = 0
    if c == '?':
        for m in range(10):
            for mod, cnt in enumerate(old):
                shifted = (mod + m * digit) % 13
                new[shifted] += cnt
    else:
        c = int(c)
        for mod, cnt in enumerate(old):
            shifted = (mod + c * digit) % 13
            new[shifted] += cnt
    for j in range(13):
        new[j] %= DIV
    new, old = old, new
    digit = (digit * 10) % 13

print(old[5])

Buggy python submission (verdict: Runtime Error):
s = input().strip()

DIV = 10**9 + 7
new = list(range(13))
old = None

if s[-1] == '?':
    old = [int(t < 10) for t in range(13)]
else:
    old = [int(t == int(c)) for t in range(13)]

digit = 10
for i, c in enumerate(reversed(s[:-1])):
    for j in range(13):
        new[j] = 0
    if c == '?':
        for m in range(10):
            for mod, cnt in enumerate(old):
                shifted = (mod + m * digit) % 13
                new[shifted] += cnt
    else:
        c = int(c)
        for mod, cnt in enumerate(old):
            shifted = (mod + c * digit) % 13
            new[shifted] += cnt
    for j in range(13):
        new[j] %= DIV
    new, old = old, new
    digit = (digit * 10) % 13

print(old[5])

Fixed submission:
s = input().strip()

DIV = 10**9 + 7
new = list(range(13))
old = None

c = s[-1]
if c == '?':
    old = [int(t < 10) for t in range(13)]
else:
    c = int(c)
    old = [int(t == c) for t in range(13)]

digit = 10
for i, c in enumerate(reversed(s[:-1])):
    for j in range(13):
        new[j] = 0
    if c == '?':
        for m in range(10):
            for mod, cnt in enumerate(old):
                shifted = (mod + m * digit) % 13
                new[shifted] += cnt
    else:
        c = int(c)
        for mod, cnt in enumerate(old):
            shifted = (mod + c * digit) % 13
            new[shifted] += cnt
    for j in range(13):
        new[j] %= DIV
    new, old = old, new
    digit = (digit * 10) % 13

print(old[5])

Buggy python submission (verdict: Time Limit Exceeded):
s = input().strip()

DIV = 10**9 + 7
digit = 1
log = []

for i, c in enumerate(reversed(s)):
    if i == 0:
        if c == '?':
            log.append([int(t < 10) for t in range(13)])
        else:
            log.append([int(t == int(c)) for t in range(13)])
    else:
        log.append([0 for t in range(13)])
        if c == '?':
            for m in range(10):
                shift = (m * digit) % 13
                for mod, cnt in enumerate(log[i - 1]):
                    shifted = (mod + shift) % 13
                    log[i][shifted] = (log[i][shifted] + cnt)
        else:
            c = int(c)
            shift = (c * digit) % 13
            for mod, cnt in enumerate(log[i - 1]):
                shifted = (mod + shift) % 13
                log[i][shifted] = (log[i][shifted] + cnt)
        log[i] = [v % DIV for v in log[i]]
    digit = (digit * 10) % 13

print(log[len(s) - 1][5])

Fixed submission:
s = input().strip()

DIV = 10**9 + 7
new = list(range(13))
old = None

c = s[-1]
if c == '?':
    old = [int(t < 10) for t in range(13)]
else:
    c = int(c)
    old = [int(t == c) for t in range(13)]

digit = 10
for i, c in enumerate(reversed(s[:-1])):
    for j in range(13):
        new[j] = 0
    if c == '?':
        for m in range(10):
            for mod, cnt in enumerate(old):
                shifted = (mod + m * digit) % 13
                new[shifted] += cnt
    else:
        c = int(c)
        for mod, cnt in enumerate(old):
            shifted = (mod + c * digit) % 13
            new[shifted] += cnt
    for j in range(13):
        new[j] %= DIV
    new, old = old, new
    digit = (digit * 10) % 13

print(old[5])

Buggy python submission (verdict: Time Limit Exceeded):
s = input().strip()

DIV = 10**9 + 7
digit = 1
log = []

for i, c in enumerate(reversed(s)):
    if i == 0:
        if c == '?':
            log.append([int(t < 10) for t in range(13)])
        else:
            log.append([int(t == int(c)) for t in range(13)])
    else:
        log.append([0 for t in range(13)])
        if c == '?':
            for m in range(10):
                shift = (m * digit) % 13
                for mod, cnt in enumerate(log[i - 1]):
                    shifted = (mod + shift) % 13
                    log[i][shifted] = (log[i][shifted] + cnt)
        else:
            c = int(c)
            shift = (c * digit) % 13
            for mod, cnt in enumerate(log[i - 1]):
                shifted = (mod + shift) % 13
                log[i][shifted] = (log[i][shifted] + cnt)
        
    digit = (digit * 10) % 13

print(log[len(s) - 1][5] % DIV)

Fixed submission:
s = input().strip()

DIV = 10**9 + 7
new = list(range(13))
old = None

c = s[-1]
if c == '?':
    old = [int(t < 10) for t in range(13)]
else:
    c = int(c)
    old = [int(t == c) for t in range(13)]

digit = 10
for i, c in enumerate(reversed(s[:-1])):
    for j in range(13):
        new[j] = 0
    if c == '?':
        for m in range(10):
            for mod, cnt in enumerate(old):
                shifted = (mod + m * digit) % 13
                new[shifted] += cnt
    else:
        c = int(c)
        for mod, cnt in enumerate(old):
            shifted = (mod + c * digit) % 13
            new[shifted] += cnt
    for j in range(13):
        new[j] %= DIV
    new, old = old, new
    digit = (digit * 10) % 13

print(old[5])

Buggy python submission (verdict: Time Limit Exceeded):
s = input().strip()

DIV = 10**9 + 7
digit = 1
log = []

for i, c in enumerate(reversed(s)):
    if i == 0:
        if c == '?':
            log.append([int(t < 10) for t in range(13)])
        else:
            log.append([int(t == int(c)) for t in range(13)])
    else:
        log.append([0 for t in range(13)])
        if c == '?':
            for m in range(10):
                shift = (m * digit) % 13
                for mod, cnt in enumerate(log[i - 1]):
                    shifted = (mod + shift) % 13
                    log[i][shifted] = (log[i][shifted] + cnt) % DIV
        else:
            c = int(c)
            shift = (c * digit) % 13
            for mod, cnt in enumerate(log[i - 1]):
                shifted = (mod + shift) % 13
                log[i][shifted] = (log[i][shifted] + cnt) % DIV
    digit = (digit * 10) % 13

print(log[len(s) - 1][5] % (10**9 + 7))

Fixed submission:
s = input().strip()

DIV = 10**9 + 7
new = list(range(13))
old = None

c = s[-1]
if c == '?':
    old = [int(t < 10) for t in range(13)]
else:
    c = int(c)
    old = [int(t == c) for t in range(13)]

digit = 10
for i, c in enumerate(reversed(s[:-1])):
    for j in range(13):
        new[j] = 0
    if c == '?':
        for m in range(10):
            for mod, cnt in enumerate(old):
                shifted = (mod + m * digit) % 13
                new[shifted] += cnt
    else:
        c = int(c)
        for mod, cnt in enumerate(old):
            shifted = (mod + c * digit) % 13
            new[shifted] += cnt
    for j in range(13):
        new[j] %= DIV
    new, old = old, new
    digit = (digit * 10) % 13

print(old[5])

Buggy python submission (verdict: Time Limit Exceeded):
s = input().strip()

DIV = 10**9 + 7
digit = 1
log = {}

for i, c in enumerate(reversed(s)):
    if i == 0:
        if c == '?':
            log[0] = {t: int(t < 10) for t in range(13)}
        else:
            log[0] = {t: int(t == int(c)) for t in range(13)}
    else:
        log[i] = {t: 0 for t in range(13)}
        if c == '?':
            for m in range(10):
                shift = (m * digit) % 13
                for mod, cnt in log[i - 1].items():
                    shifted = (mod + shift) % 13
                    log[i][shifted] = (log[i][shifted] + cnt) % DIV
        else:
            c = int(c)
            shift = (c * digit) % 13
            for mod, cnt in log[i - 1].items():
                shifted = (mod + shift) % 13
                log[i][shifted] = (log[i][shifted] + cnt) % DIV
    digit = (digit * 10) % 13

print(log[len(s) - 1][5] % (10**9 + 7))

Fixed submission:
s = input().strip()

DIV = 10**9 + 7
new = list(range(13))
old = None

c = s[-1]
if c == '?':
    old = [int(t < 10) for t in range(13)]
else:
    c = int(c)
    old = [int(t == c) for t in range(13)]

digit = 10
for i, c in enumerate(reversed(s[:-1])):
    for j in range(13):
        new[j] = 0
    if c == '?':
        for m in range(10):
            for mod, cnt in enumerate(old):
                shifted = (mod + m * digit) % 13
                new[shifted] += cnt
    else:
        c = int(c)
        for mod, cnt in enumerate(old):
            shifted = (mod + c * digit) % 13
            new[shifted] += cnt
    for j in range(13):
        new[j] %= DIV
    new, old = old, new
    digit = (digit * 10) % 13

print(old[5])

Buggy python submission (verdict: Runtime Error):
s = input().strip()

mod = 1
stable = 0
calc = {i: 0 for i in range(13)}
for c in reversed(s):
    if c == '?':
        calc[mod] += 1
    else:
        stable = (int(c) * mod + stable) % 13
    mod = (mod * 10) % 13

value = stable % 13

DIV = 10**9 + 7

# combis = {}
# def combi(n, r):
#     if r == 0:
#         return 1
#     elif (n, r) in combis:
#         return combis[n, r]
#     else:
#         res = combi(n, r - 1) * (n + 1 - r) // r
#         combis[n, r] = res
#         return res

patterns = {}
def get_pattern(d, n):
    if n == 0 or d * 9 == n:
        return 1
    elif d * 9 < n:
        return 0
    elif d == 1:
        return 1
    elif (d, n) in patterns:
        return patterns[d, n]
    else:
        res = 0
        for i in range(1, d):
            for j in range(9 * d + 1):
                res = get_pattern(i, j) * get_pattern(d-i, n-j)
        patterns[d, n] = res % DIV
        return res

def get_chance(point, value, chance):
    if point == 13:
        if value == 5:
            pat = 1
            for pt, val in enumerate(chance):
                pt += 1
                pat = (pat * get_pattern(calc[pt], val)) % DIV
            return pat
        else:
            return 0
    res = 0
    if calc[point] == 0:
        res = get_chance(point + 1, value, chance + [0])
    else:
        for i in range(calc[point] * 9 + 1):
            res += get_chance(point + 1, (value + i * point) % 13, chance + [i])
    return res

result = get_chance(1, value, [])

print(result)

Fixed submission:
s = input().strip()

DIV = 10**9 + 7
new = list(range(13))
old = None

c = s[-1]
if c == '?':
    old = [int(t < 10) for t in range(13)]
else:
    c = int(c)
    old = [int(t == c) for t in range(13)]

digit = 10
for i, c in enumerate(reversed(s[:-1])):
    for j in range(13):
        new[j] = 0
    if c == '?':
        for m in range(10):
            for mod, cnt in enumerate(old):
                shifted = (mod + m * digit) % 13
                new[shifted] += cnt
    else:
        c = int(c)
        for mod, cnt in enumerate(old):
            shifted = (mod + c * digit) % 13
            new[shifted] += cnt
    for j in range(13):
        new[j] %= DIV
    new, old = old, new
    digit = (digit * 10) % 13

print(old[5])