Buggy python submission (verdict: Time Limit Exceeded):
MOD = 1000000007

S = input()
N = len(S)

dp = [[0 for j in range(13)] for i in range(N + 1)]
dp[0][0] = 1

rem = [[0 for k in range(10)] for j in range(13)]

for j in range(13):
    for k in range(10):
        rem[j][k] = (10 * j + k) % 13

for i in range(N):
    for j in range(13):
        if S[i] == '?':
            for k in range(10):
                dp[i + 1][rem[j][k]] += dp[i][j]
                dp[i + 1][rem[j][k]] %= MOD
        else:
            k = int(S[i])
            dp[i + 1][rem[j][k]] += dp[i][j]
            dp[i + 1][rem[j][k]] %= MOD

print(dp[N][5])

Fixed submission:
S = list(input())
for i in range(len(S)):
    if S[i] != '?':
        S[i] = int(S[i])
    else:
        S[i] = -1

R = [[None]*10 for i in range(13)]
for i in range(13):
    for j in range(10):
        R[i][j] = (10*i+j) % 13

Q = [[] for i in range(13)]
for j in range(10):
    for i in range(13):
        Q[R[i][j]] += [[i,j]]

dp = [[0]*13 for i in range(len(S)+1)]
dp[0][0] = 1

for i in range(len(S)):
    for j in range(13):
        if S[i]!=-1:
            dp[i+1][j] += dp[i][Q[j][S[i]][0]]%1000000007
        else:
            for k in range(10):
                dp[i+1][j] += dp[i][Q[j][k][0]]%1000000007

print(dp[len(S)][5]%1000000007)

Buggy python submission (verdict: Time Limit Exceeded):
S = list(input())
for i in range(len(S)):
    if S[i] != '?':
        S[i] = int(S[i])
    else:
        S[i] = -1

R = [[None]*10 for i in range(13)]
for i in range(13):
    for j in range(10):
        R[i][j] = (10*i+j) % 13

Q = [[] for i in range(13)]
for j in range(10):
    for i in range(13):
        Q[R[i][j]] += [[i,j]]

dp = [[0]*13 for i in range(len(S)+1)]
dp[0][0] = 1

for i in range(len(S)):
    for j in range(13):
        if S[i]!=-1:
            dp[i+1][j] += dp[i][Q[j][S[i]][0]]
        else:
            for k in range(10):
                dp[i+1][j] += dp[i][Q[j][k][0]]

print(dp[len(S)][5]%1000000007)

Fixed submission:
S = list(input())
for i in range(len(S)):
    if S[i] != '?':
        S[i] = int(S[i])
    else:
        S[i] = -1

R = [[None]*10 for i in range(13)]
for i in range(13):
    for j in range(10):
        R[i][j] = (10*i+j) % 13

Q = [[] for i in range(13)]
for j in range(10):
    for i in range(13):
        Q[R[i][j]] += [[i,j]]

dp = [[0]*13 for i in range(len(S)+1)]
dp[0][0] = 1

for i in range(len(S)):
    for j in range(13):
        if S[i]!=-1:
            dp[i+1][j] += dp[i][Q[j][S[i]][0]]%1000000007
        else:
            for k in range(10):
                dp[i+1][j] += dp[i][Q[j][k][0]]%1000000007

print(dp[len(S)][5]%1000000007)

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

R = [[None]*10 for i in range(13)]
for i in range(13):
    for j in range(10):
        R[i][j] = (10*i+j) % 13
        
Q = [[] for i in range(13)]
for j in range(10):
    for i in range(13):
        Q[R[i][j]] += [[i,j]]

dp = [[0]*13 for i in range(len(S)+1)]
dp[0][0] = 1

for i in range(len(S)):
    for j in range(13):
        if S[i]!='?':
            dp[i+1][j] += dp[i][Q[j][int(S[i])][0]]
        else:
            for k in range(10):
                dp[i+1][j] += dp[i][Q[j][k][0]]
                
print(dp[len(S)][5]%1000000007)

Fixed submission:
S = list(input())
for i in range(len(S)):
    if S[i] != '?':
        S[i] = int(S[i])
    else:
        S[i] = -1

R = [[None]*10 for i in range(13)]
for i in range(13):
    for j in range(10):
        R[i][j] = (10*i+j) % 13

Q = [[] for i in range(13)]
for j in range(10):
    for i in range(13):
        Q[R[i][j]] += [[i,j]]

dp = [[0]*13 for i in range(len(S)+1)]
dp[0][0] = 1

for i in range(len(S)):
    for j in range(13):
        if S[i]!=-1:
            dp[i+1][j] += dp[i][Q[j][S[i]][0]]%1000000007
        else:
            for k in range(10):
                dp[i+1][j] += dp[i][Q[j][k][0]]%1000000007

print(dp[len(S)][5]%1000000007)

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

R = [[None]*10 for i in range(13)]
for i in range(13):
    for j in range(10):
        R[i][j] = (10*i+j) % 13
        
Q = [[] for i in range(13)]
for j in range(10):
    for i in range(13):
        Q[R[i][j]] += [[i,j]]

dp = [[0]*13 for i in range(len(S)+1)]
dp[0][0] = 1

for i in range(len(S)):
    for j in range(13):
        if S[i]!='?':
            dp[i+1][j] += dp[i][Q[j][int(S[i])][0]]
        else:
            for k in range(10):
                dp[i+1][j] += dp[i][Q[j][k][0]]
                
print(dp[len(S)][5]%1000000007)

Fixed submission:
S = list(input())
for i in range(len(S)):
    if S[i] != '?':
        S[i] = int(S[i])
    else:
        S[i] = -1

R = [[None]*10 for i in range(13)]
for i in range(13):
    for j in range(10):
        R[i][j] = (10*i+j) % 13

Q = [[] for i in range(13)]
for j in range(10):
    for i in range(13):
        Q[R[i][j]] += [[i,j]]

dp = [[0]*13 for i in range(len(S)+1)]
dp[0][0] = 1

for i in range(len(S)):
    for j in range(13):
        if S[i]!=-1:
            dp[i+1][j] += dp[i][Q[j][S[i]][0]]%1000000007
        else:
            for k in range(10):
                dp[i+1][j] += dp[i][Q[j][k][0]]%1000000007

print(dp[len(S)][5]%1000000007)