Buggy python submission (verdict: Time Limit Exceeded):
MOD = 10 ** 9 + 7
S = input()
dp = [0] * 13
dp[0] = 1

for i in range(len(S)):
    cdp = [0] * 13
    tmpS = 0
    if S[i] == '?':
        tmpS = -1
    else:
        tmpS = int(S[i])
    for j in range(10):
        if tmpS != -1 and tmpS != j: continue
        for k in range(13):
            cdp[(k * 10 + j) % 13] += dp[k]
            cdp[(k * 10 + j) % 13] %= MOD

    dp = cdp[:]
print(dp[5])

Fixed submission:
S = input()
INF = 10 ** 9 + 7

dp = [[0 for _ in range(13)] for _ in range(len(S) + 1)]
index = 1
dp[0][0] = 1
for i in range(len(S)):
    c = S[-i - 1]
    if c == '?':
        for j in range(10):
            for k in range(13):
                dp[i + 1][(j * index + k) % 13] += dp[i][k]
                dp[i + 1][(j * index + k) % 13] %= INF
    else:
        c = int(c)
        for k in range(13):
            dp[i + 1][(c * index + k) % 13] += dp[i][k]
            dp[i + 1][(c * index + k) % 13] %= INF
    index *= 10
    index %= 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

for i in range(len(S)):
    tmpS = 0
    if S[i] == '?':
        tmpS = -1
    else:
        tmpS = int(S[i])
    for j in range(10):
        if tmpS != -1 and tmpS != j: continue
        for k in range(13):
            dp[i + 1][(k * 10 + j) % 13] += dp[i][k]
            dp[i + 1][(k * 10 + j) % 13] %= MOD

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

Fixed submission:
S = input()
INF = 10 ** 9 + 7

dp = [[0 for _ in range(13)] for _ in range(len(S) + 1)]
index = 1
dp[0][0] = 1
for i in range(len(S)):
    c = S[-i - 1]
    if c == '?':
        for j in range(10):
            for k in range(13):
                dp[i + 1][(j * index + k) % 13] += dp[i][k]
                dp[i + 1][(j * index + k) % 13] %= INF
    else:
        c = int(c)
        for k in range(13):
            dp[i + 1][(c * index + k) % 13] += dp[i][k]
            dp[i + 1][(c * index + k) % 13] %= INF
    index *= 10
    index %= 13

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

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

dp = [[0 for _ in range(13)] for _ in range(len(S) + 1)]
index = 1
dp[0][0] = 1
for i in range(len(S)):
    c = S[-i - 1]
    if c == '?':
        for j in range(10):
            for k in range(13):
                dp[i + 1][(j * index + k) % 13] += dp[i][k]
                dp[i + 1][(j * index + k) % 13] %= INF
    else:
        c = int(c)
        for k in range(13):
            dp[i + 1][(c * index + k) % 13] += dp[i][k]
            dp[i + 1][(c * index + k) % 13] %= INF
    index *= 10
    index %= 13

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

Fixed submission:
S = input()
INF = 10 ** 9 + 7

dp = [[0 for _ in range(13)] for _ in range(len(S) + 1)]
index = 1
dp[0][0] = 1
for i in range(len(S)):
    c = S[-i - 1]
    if c == '?':
        for j in range(10):
            for k in range(13):
                dp[i + 1][(j * index + k) % 13] += dp[i][k]
                dp[i + 1][(j * index + k) % 13] %= INF
    else:
        c = int(c)
        for k in range(13):
            dp[i + 1][(c * index + k) % 13] += dp[i][k]
            dp[i + 1][(c * index + k) % 13] %= INF
    index *= 10
    index %= 13

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

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

dp = [[0 for _ in range(13)] for _ in range(len(S) + 1)]
index = 1
dp[0][0] = 1
for i in range(len(S)):
    c = S[-i - 1]
    if c == '?':
        for j in range(10):
            for k in range(13):
                dp[i + 1][(j * index + k) % 13] += dp[i][k]
                dp[i + 1][(j * index + k) % 13] %= INF
    else:
        c = int(c)
        for k in range(13):
            dp[i + 1][(c * index + k) % 13] += dp[i][k]
            dp[i + 1][(c * index + k) % 13] %= INF
    index *= 10

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

Fixed submission:
S = input()
INF = 10 ** 9 + 7

dp = [[0 for _ in range(13)] for _ in range(len(S) + 1)]
index = 1
dp[0][0] = 1
for i in range(len(S)):
    c = S[-i - 1]
    if c == '?':
        for j in range(10):
            for k in range(13):
                dp[i + 1][(j * index + k) % 13] += dp[i][k]
                dp[i + 1][(j * index + k) % 13] %= INF
    else:
        c = int(c)
        for k in range(13):
            dp[i + 1][(c * index + k) % 13] += dp[i][k]
            dp[i + 1][(c * index + k) % 13] %= INF
    index *= 10
    index %= 13

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