Buggy python submission (verdict: Time Limit Exceeded):
S = input()
N = len(S)
q = []
A = 13-5
for i in range(N-1,-1,-1):
    if S[i] == '?':
        q.append(N-i-1)
    else:
        A = (A+int(S[i])*(10**(N-i-1)))%13
DP= [[0]*13 for i in range(len(q)+1)]
DP[0][A] = 1
T = [1,10,9,12,3,4]
for i in range(len(q)):
    for j in range(13):
        for k in range(10):
            DP[i+1][(j+k*T[q[i]%6])%13] = (DP[i+1][(j+k*T[q[i]%6])%13]+DP[i][j])%(10**9+7)
print(DP[-1][0])

Fixed submission:
S = input()
N = len(S)
DP =[0]*13
DP[0] = 1
A = 0
MOD = 10**9+7

T = [1,10,9,12,3,4]
A = 0
for i in range(N):
    A*=10
    if S[i] == "?":
        hoge = [0]*13
        for j in range(13):
            for k in range(10):
                hoge[(j+k*T[(N-i-1)%6])%13] = (hoge[(j+k*T[(N-i-1)%6])%13] + DP[j])%MOD
        DP = hoge[:]
    else:
        A += int(S[i])
    A = A%13
print(DP[(5-A)%13])

Buggy python submission (verdict: Runtime Error):
S = input()
N = len(S)
DP =[0]*13
DP[0] = 1
A = 0
MOD = 10**9+7

B = [[0]*13 for i in range(13)]
for i in range(13):
    for j in range(13):
        B[i][j] = (i*j)%13
T = [1,10,9,12,3,4]
A = 0
for i in range(N):
    A*=10
    if S[i] == "?":
        hoge = [0]*13
        for j in range(13):
            for k in range(10):
                hoge[(j+k*T[(N-i-1)%6])%13] = (hoge[(j+k*T[(N-i-1)%6])%13] + DP[j])%MOD
        DP = hoge.copy()
    else:
        A = (A+int(S[i]))%13
print(DP[(A+5)%13])

Fixed submission:
S = input()
N = len(S)
DP =[0]*13
DP[0] = 1
A = 0
MOD = 10**9+7

T = [1,10,9,12,3,4]
A = 0
for i in range(N):
    A*=10
    if S[i] == "?":
        hoge = [0]*13
        for j in range(13):
            for k in range(10):
                hoge[(j+k*T[(N-i-1)%6])%13] = (hoge[(j+k*T[(N-i-1)%6])%13] + DP[j])%MOD
        DP = hoge[:]
    else:
        A += int(S[i])
    A = A%13
print(DP[(5-A)%13])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
N = len(S)
q = []
A = 13-5
for i in range(N-1,-1,-1):
    if S[i] == '?':
        q.append(N-i-1)
    else:
        A = (A+int(S[i])*(10**(N-i-1)))%13
DP= [[0]*13 for i in range(len(q)+1)]
DP[0][A] = 1
B = [[0]*13 for i in range(13)]
for i in range(13):
    for j in range(13):
        B[i][j] = (i*j)%13
T = [1,10,9,12,3,4]
for i in range(len(q)):
    for j in range(13):
        for k in range(10):
            DP[i+1][(j+k*T[q[i]%6])%13] = (DP[i+1][(j+k*T[q[i]%6])%13]+DP[i][j])%(10**9+7)
print(DP[-1][0])

Fixed submission:
S = input()
N = len(S)
DP =[0]*13
DP[0] = 1
A = 0
MOD = 10**9+7

T = [1,10,9,12,3,4]
A = 0
for i in range(N):
    A*=10
    if S[i] == "?":
        hoge = [0]*13
        for j in range(13):
            for k in range(10):
                hoge[(j+k*T[(N-i-1)%6])%13] = (hoge[(j+k*T[(N-i-1)%6])%13] + DP[j])%MOD
        DP = hoge[:]
    else:
        A += int(S[i])
    A = A%13
print(DP[(5-A)%13])

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
N = len(S)
q = []
A = 13-5
for i in range(N-1,-1,-1):
    if S[i] == '?':
        q.append(N-i-1)
    else:
        A = (A+int(S[i])*(10**(N-i-1)))%13
DP= [[0]*13 for i in range(len(q)+1)]
DP[0][A] = 1
B = [[0]*13 for i in range(13)]
for i in range(13):
    for j in range(13):
        B[i][j] = (i*j)%13
T = [1,10,9,12,3,4]
for i in range(len(q)):
    for j in range(13):
        for k in range(10):
            DP[i+1][(j+k*T[q[i]%6])%13] = (DP[i+1][(j+k*T[q[i]%6])%13]+DP[i][j])%(10**9+7)
print(DP[-1][0])
        


Fixed submission:
S = input()
N = len(S)
DP =[0]*13
DP[0] = 1
A = 0
MOD = 10**9+7

T = [1,10,9,12,3,4]
A = 0
for i in range(N):
    A*=10
    if S[i] == "?":
        hoge = [0]*13
        for j in range(13):
            for k in range(10):
                hoge[(j+k*T[(N-i-1)%6])%13] = (hoge[(j+k*T[(N-i-1)%6])%13] + DP[j])%MOD
        DP = hoge[:]
    else:
        A += int(S[i])
    A = A%13
print(DP[(5-A)%13])