Buggy python submission (verdict: Time Limit Exceeded):
p = 10**9+7
def pow(x,m):
    if m==0:
        return 1
    if m==1:
        return x%13
    if m%2==0:
        return (pow(x,m//2)**2)%13
    else:
        return (x*(pow(x,(m-1)//2)**2)%13)%13
S = input().strip()
n = len(S)
A = [0 for _ in range(n)]
for i in range(n):
    A[i] = pow(10,i)
dp = [[0 for _ in range(13)] for _ in range(n+1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if S[i]!="?":
            a = int(S[i])
            b = (a*A[n-1-i])%13
            dp[i+1][j] = dp[i][(j-b)%13]
        else:
            for k in range(10):
                b = (k*A[n-1-i])%13
                dp[i+1][j] = (dp[i+1][j]+dp[i][(j-b)%13])%p
print(dp[n][5])

Fixed submission:
p = 10**9+7
S = input().strip()
n = len(S)
dp = [[0 for _ in range(13)] for _ in range(n+1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if S[i]!="?":
            dp[i+1][(10*j+int(S[i]))%13] = dp[i][j]
        else:
            for k in range(10):
                dp[i+1][(10*j+k)%13] = (dp[i+1][(10*j+k)%13]+dp[i][j])%p
print(dp[n][5])

Buggy python submission (verdict: Time Limit Exceeded):
p = 10**9+7
def pow(x,m):
    if m==0:
        return 1
    if m==1:
        return x
    if m%2==0:
        return (pow(x,m//2)**2)%13
    else:
        return (x*(pow(x,(m-1)//2)**2)%13)%13
S = input().strip()
n = len(S)
A = [0 for _ in range(n)]
for i in range(n):
    A[i] = pow(10,i)
dp = [[0 for _ in range(13)] for _ in range(n+1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if S[i]!="?":
            a = int(S[i])
            b = (a*A[n-1-i])%13
            dp[i+1][j] = dp[i][(j-b)%13]
        else:
            for k in range(10):
                b = (k*A[n-1-i])%13
                dp[i+1][j] = (dp[i+1][j]+dp[i][(j-b)%13])%p
print(dp[n][5])

Fixed submission:
p = 10**9+7
S = input().strip()
n = len(S)
dp = [[0 for _ in range(13)] for _ in range(n+1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if S[i]!="?":
            dp[i+1][(10*j+int(S[i]))%13] = dp[i][j]
        else:
            for k in range(10):
                dp[i+1][(10*j+k)%13] = (dp[i+1][(10*j+k)%13]+dp[i][j])%p
print(dp[n][5])

Buggy python submission (verdict: Time Limit Exceeded):
p = 10**9+7
def pow(x,m):
    if m==0:
        return 1
    if m==1:
        return x
    if m%2==0:
        return (pow(x,m//2)**2)%13
    else:
        return (x*(pow(x,(m-1)//2)**2)%13)%13
S = input().strip()
n = len(S)
A = [0 for _ in range(n)]
for i in range(n):
    A[i] = pow(10,i)
dp = [[0 for _ in range(13)] for _ in range(n+1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if S[i]!="?":
            a = int(S[i])
            b = (a*A[n-1-i])%13
            dp[i+1][j] = dp[i][(j-b)%13]
        else:
            for k in range(10):
                b = (k*A[n-1-i])%13
                dp[i+1][j] = (dp[i+1][j]+dp[i][(j-b)%13])%p
print(dp[n][5])

Fixed submission:
p = 10**9+7
S = input().strip()
n = len(S)
dp = [[0 for _ in range(13)] for _ in range(n+1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if S[i]!="?":
            dp[i+1][(10*j+int(S[i]))%13] = dp[i][j]
        else:
            for k in range(10):
                dp[i+1][(10*j+k)%13] = (dp[i+1][(10*j+k)%13]+dp[i][j])%p
print(dp[n][5])

Buggy python submission (verdict: Time Limit Exceeded):
p = 10**9+7
def pow(x,m):
    if m==0:
        return 1
    if m==1:
        return x
    if m%2==0:
        return (pow(x,m//2)**2)%13
    else:
        return (x*(pow(x,(m-1)//2)**2)%13)%13
S = input().strip()
n = len(S)
dp = [[0 for _ in range(13)] for _ in range(n+1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if S[i]!="?":
            a = int(S[i])
            b = (a*pow(10,n-1-i))%13
            dp[i+1][j] = dp[i][(j-b)%13]
        else:
            for k in range(10):
                b = (k*pow(10,n-1-i))%13
                dp[i+1][j] = (dp[i+1][j]+dp[i][(j-b)%13])%p
print(dp[n][5])

Fixed submission:
p = 10**9+7
S = input().strip()
n = len(S)
dp = [[0 for _ in range(13)] for _ in range(n+1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if S[i]!="?":
            dp[i+1][(10*j+int(S[i]))%13] = dp[i][j]
        else:
            for k in range(10):
                dp[i+1][(10*j+k)%13] = (dp[i+1][(10*j+k)%13]+dp[i][j])%p
print(dp[n][5])

Buggy python submission (verdict: Time Limit Exceeded):
p = 10**9+7
def pow(x,m):
    if m==0:
        return 1
    if m==1:
        return x
    if m%2==0:
        return (pow(x,m//2)**2)%13
    else:
        return (x*(pow(x,(m-1)//2)**2)%13)%13
S = input().strip()
n = len(S)
dp = [[0 for _ in range(13)] for _ in range(n+1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if S[i]!="?":
            a = int(S[i])
            b = (a*pow(10,n-1-i))%13
            dp[i+1][j] = dp[i][(j-b)%13]
        else:
            for k in range(10):
                b = (k*pow(10,n-1-i))%13
                dp[i+1][j] = (dp[i+1][j]+dp[i][(j-b)%13])%p
print(dp[n][5])

Fixed submission:
p = 10**9+7
S = input().strip()
n = len(S)
dp = [[0 for _ in range(13)] for _ in range(n+1)]
dp[0][0] = 1
for i in range(n):
    for j in range(13):
        if S[i]!="?":
            dp[i+1][(10*j+int(S[i]))%13] = dp[i][j]
        else:
            for k in range(10):
                dp[i+1][(10*j+k)%13] = (dp[i+1][(10*j+k)%13]+dp[i][j])%p
print(dp[n][5])