Buggy python submission (verdict: Time Limit Exceeded):
def main():
    s = input()
    mod = 1000000007
    n = len(s)
    dp = [[0]*13 for i in range(n+1)]
    dp[0][0] = 1
    k = 1
    cnt = 0
    for i in range(n):
        t = 0
        for j in range(10):
            if s[n-i-1]=="?":
                for l in range(13):
                    dp[i+1][(l+t)%13]+=dp[i][l]
                    if cnt%1000==0:
                        dp[i+1][(l+t)%13]%=mod
            elif int(s[n-i-1])==j:
                for l in range(13):
                    dp[i+1][(l+t)%13]+=dp[i][l]
                    if cnt%1000==0:
                        dp[i+1][(l+t)%13]%=mod
            t+=k
            if t>=13:
                t-=13
            cnt+=1
        k=t
    print(dp[n][5]%mod)

if __name__ == '__main__':
    main()

Fixed submission:
s = input()
mod = 1000000007
n = len(s)
dp = [[0]*13 for i in range(n+1)]
dp[0][0] = 1
k = 1
for i in range(n):
    t = 0
    for j in range(10):
        if s[n-i-1]=="?":
            for l in range(13):
                dp[i+1][(l+t)%13]+=dp[i][l]
                dp[i+1][(l+t)%13]%=mod
        elif int(s[n-i-1])==j:
            for l in range(13):
                dp[i+1][(l+t)%13]+=dp[i][l]
                dp[i+1][(l+t)%13]%=mod
        t+=k
        t%=13
    k=t
print(dp[n][5])

Buggy python submission (verdict: Time Limit Exceeded):
def main():
    s = input()
    mod = 1000000007
    n = len(s)
    dp = [[0]*13 for i in range(n+1)]
    dp[0][0] = 1
    k = 1
    for i in range(n):
        t = 0
        for j in range(10):
            if s[n-i-1]=="?":
                for l in range(13):
                    dp[i+1][(l+t)%13]+=dp[i][l]
                    dp[i+1][(l+t)%13]%=mod
            elif int(s[n-i-1])==j:
                for l in range(13):
                    dp[i+1][(l+t)%13]+=dp[i][l]
                    dp[i+1][(l+t)%13]%=mod
            t+=k
            t%=13
        k=t
    print(dp[n][5])

if __name__ == '__main__':
    main()

Fixed submission:
s = input()
mod = 1000000007
n = len(s)
dp = [[0]*13 for i in range(n+1)]
dp[0][0] = 1
k = 1
for i in range(n):
    t = 0
    for j in range(10):
        if s[n-i-1]=="?":
            for l in range(13):
                dp[i+1][(l+t)%13]+=dp[i][l]
                dp[i+1][(l+t)%13]%=mod
        elif int(s[n-i-1])==j:
            for l in range(13):
                dp[i+1][(l+t)%13]+=dp[i][l]
                dp[i+1][(l+t)%13]%=mod
        t+=k
        t%=13
    k=t
print(dp[n][5])

Buggy python submission (verdict: Time Limit Exceeded):
s = input()
mod = 1000000007
n = len(s)
dp = [[0]*13 for i in range(n+1)]
dp[0][0] = 1
k = 1
for i in range(n):
    t = 0
    for j in range(10):
        if s[n-i-1]=="?":
            for l in range(13):
                dp[i+1][(l+t)%13]+=dp[i][l]
                dp[i+1][(l+t)%13]%=mod
        elif int(s[n-i-1])==j:
            for l in range(13):
                dp[i+1][(l+t)%13]+=dp[i][l]
                dp[i+1][(l+t)%13]%=mod
        t+=k
        t%=13
    k=t
print(dp[n][5])

Fixed submission:
s = input()
mod = 1000000007
n = len(s)
dp = [[0]*13 for i in range(n+1)]
dp[0][0] = 1
k = 1
for i in range(n):
    t = 0
    for j in range(10):
        if s[n-i-1]=="?":
            for l in range(13):
                dp[i+1][(l+t)%13]+=dp[i][l]
                dp[i+1][(l+t)%13]%=mod
        elif int(s[n-i-1])==j:
            for l in range(13):
                dp[i+1][(l+t)%13]+=dp[i][l]
                dp[i+1][(l+t)%13]%=mod
        t+=k
        t%=13
    k=t
print(dp[n][5])