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

for S in sys.stdin:
    break
S = S.strip()
le = len(S)

mod = 10**9 + 7

mo = 1

dp = ([1]*10 if S[-1] == "?" else [int(x == int(S[-1])) for x in range(10)]) + [0]*3

i = 1
while i != le:
    mo = (mo * 10)%13
    a = [0]*13
    if S[-i-1] == "?":
        j = 0
        while j != 10:
            k = 0
            while k != 13:
                a[(k+mo*j)%13] += dp[k]
                a[(k+mo*j)%13] %= mod
                k += 1
            j += 1
    else:
        j = int(S[-i-1])
        k = 0
        while k != 13:
            a[(k+mo*j)%13] += dp[k]
            a[(k+mo*j)%13] %= mod
            k += 1
    dp = a
    i += 1

print(dp[5])

Fixed submission:
import sys

for S in sys.stdin:
    break
S = S.strip()
le = len(S)

mod = 10**9 + 7

mo = 1

dp = ([1]*10 if S[-1] == "?" else [int(x == int(S[-1])) for x in range(10)]) + [0]*3

i = 1
while i != le:
    mo = (mo * 10)%13
    a = [0]*13
    if S[-i-1] == "?":
        j = 0
        while j != 10:
            k = 0
            while k != 13:
                a[(k+mo*j)%13] += dp[k]
                a[(k+mo*j)%13] %= mod
                k += 1
            j += 1
    else:
        j = int(S[-i-1])
        k = 0
        while k != 13:
            a[(k+mo*j)%13] += dp[k]
            a[(k+mo*j)%13] %= mod
            k += 1
    dp = a
    i += 1

print(dp[5])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
le = len(S)

mod = 10**9 + 7

mo = 1

dp = ([1]*10 if S[-1] == "?" else [int(x == int(S[-1])) for x in range(10)]) + [0]*3

i = 1
while i != le:
    mo = (mo * 10)%13
    a = [0]*13
    if S[-i-1] == "?":
        j = 0
        while j != 10:
            k = 0
            while k != 13:
                a[(k+mo*j)%13] += dp[k]
                a[(k+mo*j)%13] %= mod
                k += 1
            j += 1
    else:
        j = int(S[-i-1])
        k = 0
        while k != 13:
            a[(k+mo*j)%13] += dp[k]
            a[(k+mo*j)%13] %= mod
            k += 1
    dp = a
    i += 1

print(dp[5])

Fixed submission:
import sys

for S in sys.stdin:
    break
S = S.strip()
le = len(S)

mod = 10**9 + 7

mo = 1

dp = ([1]*10 if S[-1] == "?" else [int(x == int(S[-1])) for x in range(10)]) + [0]*3

i = 1
while i != le:
    mo = (mo * 10)%13
    a = [0]*13
    if S[-i-1] == "?":
        j = 0
        while j != 10:
            k = 0
            while k != 13:
                a[(k+mo*j)%13] += dp[k]
                a[(k+mo*j)%13] %= mod
                k += 1
            j += 1
    else:
        j = int(S[-i-1])
        k = 0
        while k != 13:
            a[(k+mo*j)%13] += dp[k]
            a[(k+mo*j)%13] %= mod
            k += 1
    dp = a
    i += 1

print(dp[5])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
le = len(S)
S = S[::-1]

mod = 10**9 + 7

mo = 1

dp = ([1]*10 if S[0] == "?" else [int(x == int(S[0])) for x in range(10)]) + [0]*3

i = 1
while i != le:
    mo = (mo * 10)%13
    a = [0]*13
    if S[i] == "?":
        j = 0
        while j != 10:
            k = 0
            while k != 13:
                a[(k+mo*j)%13] += dp[k]
                a[(k+mo*j)%13] %= mod
                k += 1
            j += 1
    else:
        j = int(S[i])
        k = 0
        while k != 13:
            a[(k+mo*j)%13] += dp[k]
            a[(k+mo*j)%13] %= mod
            k += 1
    dp = a
    i += 1

print(dp[5])

Fixed submission:
import sys

for S in sys.stdin:
    break
S = S.strip()
le = len(S)

mod = 10**9 + 7

mo = 1

dp = ([1]*10 if S[-1] == "?" else [int(x == int(S[-1])) for x in range(10)]) + [0]*3

i = 1
while i != le:
    mo = (mo * 10)%13
    a = [0]*13
    if S[-i-1] == "?":
        j = 0
        while j != 10:
            k = 0
            while k != 13:
                a[(k+mo*j)%13] += dp[k]
                a[(k+mo*j)%13] %= mod
                k += 1
            j += 1
    else:
        j = int(S[-i-1])
        k = 0
        while k != 13:
            a[(k+mo*j)%13] += dp[k]
            a[(k+mo*j)%13] %= mod
            k += 1
    dp = a
    i += 1

print(dp[5])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
le = len(S)
S = S[::-1]

mod = 10**9 + 7

dp = [0] * (le)
modi = [1] * le
for i in range(le-1):
    modi[i+1] = (modi[i] * 10)%13

dp[0] = ([1]*10 if S[0] == "?" else [int(x == int(S[0])) for x in range(10)]) + [0]*3

for i in range(1,le):
    mo = modi[i]
    a = [0]*13
    b = dp[i-1]
    for j in range(10) if S[i] == "?" else [int(S[i])]:
        for k in range(13):
            a[(k+mo*j)%13] += b[k]
            a[(k+mo*j)%13] %= mod
    dp[i] = a

print(dp[-1][5])

Fixed submission:
import sys

for S in sys.stdin:
    break
S = S.strip()
le = len(S)

mod = 10**9 + 7

mo = 1

dp = ([1]*10 if S[-1] == "?" else [int(x == int(S[-1])) for x in range(10)]) + [0]*3

i = 1
while i != le:
    mo = (mo * 10)%13
    a = [0]*13
    if S[-i-1] == "?":
        j = 0
        while j != 10:
            k = 0
            while k != 13:
                a[(k+mo*j)%13] += dp[k]
                a[(k+mo*j)%13] %= mod
                k += 1
            j += 1
    else:
        j = int(S[-i-1])
        k = 0
        while k != 13:
            a[(k+mo*j)%13] += dp[k]
            a[(k+mo*j)%13] %= mod
            k += 1
    dp = a
    i += 1

print(dp[5])