Buggy python submission (verdict: Time Limit Exceeded):
S = input()
INF = 10 ** 9 + 7
mod = [1,10,9,12,3,4]
dp = [[0 for _ in range(13)] for l in range(len(S))]
S_li = [_ for _ in S]
S_li = S_li[::-1]
if S_li[0] == '?':
    dp[0][0:10] = [1,1,1,1,1,1,1,1,1,1]
else:
    dp[0][int(S_li[0])] = 1
for _ in range(1,len(S)):
    if S_li[_] == '?':
        for x in range(10):
            for y in range(13):
                dp[_][(x * mod[_ % 6] + y) % 13] += dp[_ - 1][y] % INF
    else:
        for y in range(13):
            dp[_][(int(S_li[_]) * mod[_ % 6] + y) % 13] += dp[_ - 1][y] % INF
print(dp[-1][5] % INF)

Fixed submission:
MOD = 1000000007;
 
s = [int(x) if x!="?" else -1 for x in input()]
#print(s)
n=len(s)
 
r=[0]*13
 
c=s[0]
if (c!=-1):
    r[c]=1
else:
    for i in range(10):r[i]=1
for i in range(1,n):
    dp=[0]*26
    for j in range(13):dp[j*10%13]+=(r[j]%MOD)
    dp[13:26]=dp[0:13]
    c=s[i]
    r=[0]*13
    if (c==-1):
        w=sum(dp[4:14])
        for j in range(13):
            r[j]+=w
            w=w+dp[j+1]-dp[4+j]
    else:
        for j in range(13):
            r[j]+=dp[13-c+j]
print (r[5]%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
INF = 10 ** 9 + 7
dp = [[0 for _ in range(13)] for l in range(len(S))]
S_li = [_ for _ in S]
S_li = S_li[::-1]
if S_li[0] == '?':
    dp[0][0:10] = [1,1,1,1,1,1,1,1,1,1]
else:
    dp[0][int(S_li[0])] = 1
for _ in range(1,len(S)):
    if S_li[_] == '?':
        for x in range(10):
            for y in range(13):
                dp[_][((x * (10 ** (_ % 6))) + y) % 13] += dp[_ - 1][y] % INF
    else:
        for y in range(13):
            dp[_][((int(S_li[_]) * (10 ** (_ % 6))) + y) % 13] += dp[_ - 1][y] % INF
print(dp[-1][5] % INF)

Fixed submission:
MOD = 1000000007;
 
s = [int(x) if x!="?" else -1 for x in input()]
#print(s)
n=len(s)
 
r=[0]*13
 
c=s[0]
if (c!=-1):
    r[c]=1
else:
    for i in range(10):r[i]=1
for i in range(1,n):
    dp=[0]*26
    for j in range(13):dp[j*10%13]+=(r[j]%MOD)
    dp[13:26]=dp[0:13]
    c=s[i]
    r=[0]*13
    if (c==-1):
        w=sum(dp[4:14])
        for j in range(13):
            r[j]+=w
            w=w+dp[j+1]-dp[4+j]
    else:
        for j in range(13):
            r[j]+=dp[13-c+j]
print (r[5]%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
INF = 10 ** 9 + 7
dp = [[0 for _ in range(13)] for l in range(len(S))]
S_li = [_ for _ in S]
S_li = S_li[::-1]
if S_li[0] == '?':
    dp[0][0:10] = [1,1,1,1,1,1,1,1,1,1]
else:
    dp[0][int(S_li[0])] = 1
for _ in range(1,len(S)):
    if S_li[_] == '?':
        for x in range(10):
            for y in range(13):
                dp[_][((x * (10 ** _)) + y) % 13] += dp[_ - 1][y] % INF
    else:
        for y in range(13):
            dp[_][((int(S_li[_]) * (10 ** _)) + y) % 13] += dp[_ - 1][y] % INF
print(dp[-1][5] % INF)

Fixed submission:
MOD = 1000000007;
 
s = [int(x) if x!="?" else -1 for x in input()]
#print(s)
n=len(s)
 
r=[0]*13
 
c=s[0]
if (c!=-1):
    r[c]=1
else:
    for i in range(10):r[i]=1
for i in range(1,n):
    dp=[0]*26
    for j in range(13):dp[j*10%13]+=(r[j]%MOD)
    dp[13:26]=dp[0:13]
    c=s[i]
    r=[0]*13
    if (c==-1):
        w=sum(dp[4:14])
        for j in range(13):
            r[j]+=w
            w=w+dp[j+1]-dp[4+j]
    else:
        for j in range(13):
            r[j]+=dp[13-c+j]
print (r[5]%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
dp = [[0 for _ in range(13)] for l in range(len(S))]
S_li = [_ for _ in S]
S_li = S_li[::-1]
if S_li[0] == '?':
    dp[0][0:10] = [1,1,1,1,1,1,1,1,1,1]
else:
    dp[0][int(S_li[0])] = 1
for _ in range(1,len(S)):
    if S_li[_] == '?':
        for x in range(10):
            for y in range(13):
                dp[_][((x * (10 ** _)) + y) % 13] += dp[_ - 1][y] 
    else:
        for y in range(13):
            dp[_][((int(S_li[_]) * (10 ** _)) + y) % 13] += dp[_ - 1][y] 
print(dp[-1][5] % ((10 ** 9) + 7))

Fixed submission:
MOD = 1000000007;
 
s = [int(x) if x!="?" else -1 for x in input()]
#print(s)
n=len(s)
 
r=[0]*13
 
c=s[0]
if (c!=-1):
    r[c]=1
else:
    for i in range(10):r[i]=1
for i in range(1,n):
    dp=[0]*26
    for j in range(13):dp[j*10%13]+=(r[j]%MOD)
    dp[13:26]=dp[0:13]
    c=s[i]
    r=[0]*13
    if (c==-1):
        w=sum(dp[4:14])
        for j in range(13):
            r[j]+=w
            w=w+dp[j+1]-dp[4+j]
    else:
        for j in range(13):
            r[j]+=dp[13-c+j]
print (r[5]%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
S = input()
dp = [[0 for _ in range(13)] for l in range(len(S))]
S_li = [_ for _ in S]
S_li = S_li[::-1]
if S_li[0] == '?':
    dp[0][0:10] = [1,1,1,1,1,1,1,1,1,1]
else:
    dp[0][int(S_li[0])] = 1
for _ in range(1,len(S)):
    if S_li[_] == '?':
        for x in range(10):
            for y in range(13):
                dp[_][((x * (10 ** _)) + y) % 13] += dp[_ - 1][y] 
    else:
        for y in range(13):
            dp[_][((int(S_li[_]) * (10 ** _)) + y) % 13] += dp[_ - 1][y] 
print(dp[-1][5] % ((10 ** 9) + 7))

Fixed submission:
MOD = 1000000007;
 
s = [int(x) if x!="?" else -1 for x in input()]
#print(s)
n=len(s)
 
r=[0]*13
 
c=s[0]
if (c!=-1):
    r[c]=1
else:
    for i in range(10):r[i]=1
for i in range(1,n):
    dp=[0]*26
    for j in range(13):dp[j*10%13]+=(r[j]%MOD)
    dp[13:26]=dp[0:13]
    c=s[i]
    r=[0]*13
    if (c==-1):
        w=sum(dp[4:14])
        for j in range(13):
            r[j]+=w
            w=w+dp[j+1]-dp[4+j]
    else:
        for j in range(13):
            r[j]+=dp[13-c+j]
print (r[5]%MOD)