Buggy python submission (verdict: Time Limit Exceeded):
S=input()
N=len(S)
Sinfo=''
for i in range(0,N):
    if S[i]=='?':
        Sinfo+='0'
    else:
        Sinfo+=S[i]
first=int(Sinfo)%13
count=0
hatenadata=[]
for i in range(0,N):
    if S[i]=='?':
        count+=1
        hatenadata.append(i)

dp=[[0 for i in range(0,13)] for i in range(0,count+1)]

for i in range(0,13):
    if first==i:
        dp[0][i]=1

for i in range(1,count+1):
    digit=N-hatenadata[i-1]
    for j in range(0,13):
        dp[i][j]=sum(dp[i-1][(j-k*10**((digit-1)%6))%13] for k in range(0,10))%(10**9+7)

print(dp[count][5]%(10**9+7))


Fixed submission:
S=input()
N=len(S)
count=0
hatenadata=[]
Sinfo=[]
for i in range(0,N):
    if S[i]=='?':
        Sinfo.append('0')
        count+=1
        hatenadata.append(i)
    else:
        Sinfo.append(S[i])
X=''.join(Sinfo)
first=int(X)%13

dp=[[0 for i in range(0,13)] for i in range(0,count+1)]

for i in range(0,13):
    if first==i:
        dp[0][i]=1

for i in range(1,count+1):
    digit=N-hatenadata[i-1]
    for j in range(0,13):
        dp[i][j]=sum(dp[i-1][(j-k*10**((digit-1)%6))%13] for k in range(0,10))%(10**9+7)

print(dp[count][5]%(10**9+7))

Buggy python submission (verdict: Time Limit Exceeded):
S=input()
N=len(S)
Sinfo=''
for i in range(0,N):
    if S[i]=='?':
        Sinfo+='0'
    else:
        Sinfo+=S[i]
first=int(Sinfo)%13
count=0
hatenadata=[]
for i in range(0,N):
    if S[i]=='?':
        count+=1
        hatenadata.append(i)

r=[[(i*10**(j-1))%13 for i in range(0,10)] for j in range(1,7)]

dp=[[0 for i in range(0,13)] for i in range(0,count+1)]

for i in range(0,13):
    if first==i:
        dp[0][i]=1

for i in range(1,count+1):
    digit=N-hatenadata[i-1]
    for j in range(0,13):
        dp[i][j]=sum(dp[i-1][(j-r[(digit-1)%6][k])%13] for k in range(0,10))%(10**9+7)


print(dp[count][5]%(10**9+7))


Fixed submission:
S=input()
N=len(S)
count=0
hatenadata=[]
Sinfo=[]
for i in range(0,N):
    if S[i]=='?':
        Sinfo.append('0')
        count+=1
        hatenadata.append(i)
    else:
        Sinfo.append(S[i])
X=''.join(Sinfo)
first=int(X)%13

dp=[[0 for i in range(0,13)] for i in range(0,count+1)]

for i in range(0,13):
    if first==i:
        dp[0][i]=1

for i in range(1,count+1):
    digit=N-hatenadata[i-1]
    for j in range(0,13):
        dp[i][j]=sum(dp[i-1][(j-k*10**((digit-1)%6))%13] for k in range(0,10))%(10**9+7)

print(dp[count][5]%(10**9+7))

Buggy python submission (verdict: Time Limit Exceeded):
S=input()
N=len(S)
Sinfo=''
for i in range(0,N):
    if S[i]=='?':
        Sinfo+='0'
    else:
        Sinfo+=S[i]
first=int(Sinfo)%13
count=0
hatenadata=[]
for i in range(0,N):
    if S[i]=='?':
        count+=1
        hatenadata.append(i)

r=[[(i*10**(j-1))%13 for i in range(0,10)] for j in range(1,7)]

dp=[[0 for i in range(0,13)] for i in range(0,count+1)]

for i in range(0,13):
    if first==i:
        dp[0][i]=1

for i in range(1,count+1):
    digit=N-hatenadata[i-1]
    for j in range(0,13):
        dp[i][j]=sum(dp[i-1][(j-r[(digit-1)%6][k])%13] for k in range(0,10))


print(dp[count][5]%(10**9+7))

Fixed submission:
S=input()
N=len(S)
count=0
hatenadata=[]
Sinfo=[]
for i in range(0,N):
    if S[i]=='?':
        Sinfo.append('0')
        count+=1
        hatenadata.append(i)
    else:
        Sinfo.append(S[i])
X=''.join(Sinfo)
first=int(X)%13

dp=[[0 for i in range(0,13)] for i in range(0,count+1)]

for i in range(0,13):
    if first==i:
        dp[0][i]=1

for i in range(1,count+1):
    digit=N-hatenadata[i-1]
    for j in range(0,13):
        dp[i][j]=sum(dp[i-1][(j-k*10**((digit-1)%6))%13] for k in range(0,10))%(10**9+7)

print(dp[count][5]%(10**9+7))

Buggy python submission (verdict: Time Limit Exceeded):
S=input()
N=len(S)
Sinfo=''
for i in range(0,N):
    if S[i]=='?':
        Sinfo+='0'
    else:
        Sinfo+=S[i]
first=int(Sinfo)%13
count=0
hatenadata=[]
for i in range(0,N):
    if S[i]=='?':
        count+=1
        hatenadata.append(i)

r=[[(i*10**(j-1))%13 for i in range(0,10)] for j in range(1,7)]

dp=[[0 for i in range(0,13)] for i in range(0,count+1)]

for i in range(0,13):
    if first==i:
        dp[0][i]=1

for i in range(1,count+1):
    digit=N-hatenadata[i-1]
    for j in range(0,13):
        dp[i][j]=sum(dp[i-1][(j-r[(digit-1)%6][k])%13] for k in range(0,10))


print(dp[count][5]%(10**9+7))

Fixed submission:
S=input()
N=len(S)
count=0
hatenadata=[]
Sinfo=[]
for i in range(0,N):
    if S[i]=='?':
        Sinfo.append('0')
        count+=1
        hatenadata.append(i)
    else:
        Sinfo.append(S[i])
X=''.join(Sinfo)
first=int(X)%13

dp=[[0 for i in range(0,13)] for i in range(0,count+1)]

for i in range(0,13):
    if first==i:
        dp[0][i]=1

for i in range(1,count+1):
    digit=N-hatenadata[i-1]
    for j in range(0,13):
        dp[i][j]=sum(dp[i-1][(j-k*10**((digit-1)%6))%13] for k in range(0,10))%(10**9+7)

print(dp[count][5]%(10**9+7))