Buggy python submission (verdict: Time Limit Exceeded):
S = input()
dp = [[0]*13 for _ in range(len(S))]
mod = 10**9+7
for i in range(13):
    if S[0] == "?":
        dp[0][i] = 1 if i <= 9 else 0
    else:
        dp[0][i] = 1 if int(S[0]) == i else 0
for i in range(1,len(S)):
    if S[i] == "?":
        for j in range(10):
            for k in range(13):
                dp[i][(k*10+j) % 13] = (dp[i][(k*10+j) % 13]+dp[i-1][k])%mod
    else:
        j = int(S[i])
        for k in range(13):
            dp[i][(k*10+j)%13] = (dp[i][(k*10+j)%13]+dp[i-1][k])%mod
print(dp[len(S)-1][5])

Fixed submission:
S = input()
dp = [[0]*13 for _ in range(len(S))]
mod = 10**9+7
for i in range(13):
    if S[0] == "?":
        dp[0][i] = 1 if i <= 9 else 0
    else:
        dp[0][i] = 1 if int(S[0]) == i else 0
for i in range(1,len(S)):
    if S[i] == "?":
        for j in range(10):
            for k in range(13):
                dp[i][(k*10+j) % 13] = (dp[i][(k*10+j) % 13]+dp[i-1][k])%mod
    else:
        j = int(S[i])
        for k in range(13):
            dp[i][(k*10+j)%13] = (dp[i][(k*10+j)%13]+dp[i-1][k])%mod
print(dp[len(S)-1][5])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(1000000)

ls = [0,4,8,12,3,7,11,2,6,10,1,5,9]
S = input()
dp = [[None]*13 for _ in range(len(S))]
mod = 10**9+7
def f(i, r):
    if dp[i][r] != None:
        return dp[i][r]
    if i == 0:
        if S[0] == "?":
            dp[i][r] = 1 if r <= 9 else 0
            return dp[i][r]
        else:
            dp[i][r] = 1 if int(S[0]) == r else 0
            return dp[i][r]
    if S[i] != "?":
        c = int(S[i])
        tmp = (r-c) % 13
        dp[i][r] = f(i-1, ls[tmp]) % mod 
        return dp[i][r]
    else:
        ans = 0
        for j in range(10):
            tmp = (r-j) % 13
            ans = (ans +f(i-1, ls[tmp])) % mod
        dp[i][r] = ans % mod
        return dp[i][r]

print(f(len(S)-1, 5))


Fixed submission:
S = input()
dp = [[0]*13 for _ in range(len(S))]
mod = 10**9+7
for i in range(13):
    if S[0] == "?":
        dp[0][i] = 1 if i <= 9 else 0
    else:
        dp[0][i] = 1 if int(S[0]) == i else 0
for i in range(1,len(S)):
    if S[i] == "?":
        for j in range(10):
            for k in range(13):
                dp[i][(k*10+j) % 13] = (dp[i][(k*10+j) % 13]+dp[i-1][k])%mod
    else:
        j = int(S[i])
        for k in range(13):
            dp[i][(k*10+j)%13] = (dp[i][(k*10+j)%13]+dp[i-1][k])%mod
print(dp[len(S)-1][5])

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(1000000)

ls = [0,4,8,12,3,7,11,2,6,10,1,5,9]
S = input()
dp = [[None]*13 for _ in range(len(S))]
mod = 10**9+7
def f(i, r):
    if dp[i][r] != None:
        return dp[i][r]
    if i == 0:
        if S[0] == "?":
            dp[i][r] = 1 if r <= 9 else 0
            return dp[i][r]
        else:
            dp[i][r] = 1 if int(S[0]) == r else 0
            return dp[i][r]
    if S[i] != "?":
        c = int(S[i])
        tmp = (r-c) % 13
        dp[i][r] = f(i-1, ls[tmp]) % mod 
        return dp[i][r]
    else:
        ans = 0
        for j in range(10):
            tmp = (r-j) % 13
            ans = (ans +f(i-1, ls[tmp])) % mod
        dp[i][r] = ans % mod
        return dp[i][r]

print(f(len(S)-1, 5))


Fixed submission:
S = input()
dp = [[0]*13 for _ in range(len(S))]
mod = 10**9+7
for i in range(13):
    if S[0] == "?":
        dp[0][i] = 1 if i <= 9 else 0
    else:
        dp[0][i] = 1 if int(S[0]) == i else 0
for i in range(1,len(S)):
    if S[i] == "?":
        for j in range(10):
            for k in range(13):
                dp[i][(k*10+j) % 13] = (dp[i][(k*10+j) % 13]+dp[i-1][k])%mod
    else:
        j = int(S[i])
        for k in range(13):
            dp[i][(k*10+j)%13] = (dp[i][(k*10+j)%13]+dp[i-1][k])%mod
print(dp[len(S)-1][5])

Buggy python submission (verdict: Runtime Error):
import sys
sys.setrecursionlimit(10000)

ls = [0,4,8,12,3,7,11,2,6,10,1,5,9]
S = input()
dp = [[None]*13 for _ in range(len(S))]
mod = 10**9+7
def f(i, r):
    if dp[i][r] != None:
        return dp[i][r]
    if i == 0:
        if S[0] == "?":
            dp[i][r] = 1 if r <= 9 else 0
            return dp[i][r]
        else:
            dp[i][r] = 1 if int(S[0]) == r else 0
            return dp[i][r]
    if S[i] != "?":
        c = int(S[i])
        tmp = (r-c) % 13
        dp[i][r] = f(i-1, ls[tmp]) % mod 
        return dp[i][r]
    else:
        ans = 0
        for j in range(10):
            tmp = (r-j) % 13
            ans = (ans +f(i-1, ls[tmp])) % mod
        dp[i][r] = ans % mod
        return dp[i][r]

print(f(len(S)-1, 5))


Fixed submission:
S = input()
dp = [[0]*13 for _ in range(len(S))]
mod = 10**9+7
for i in range(13):
    if S[0] == "?":
        dp[0][i] = 1 if i <= 9 else 0
    else:
        dp[0][i] = 1 if int(S[0]) == i else 0
for i in range(1,len(S)):
    if S[i] == "?":
        for j in range(10):
            for k in range(13):
                dp[i][(k*10+j) % 13] = (dp[i][(k*10+j) % 13]+dp[i-1][k])%mod
    else:
        j = int(S[i])
        for k in range(13):
            dp[i][(k*10+j)%13] = (dp[i][(k*10+j)%13]+dp[i-1][k])%mod
print(dp[len(S)-1][5])