Buggy python submission (verdict: Time Limit Exceeded):

def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        if s[i]=="?":
            for k in range(13):
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            continue
        else:
            number=int(s[i])
            for k in range(13):
                dp[i][k]=dp[i-1][U[k][number]]
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        if s[i]=="?":
            for k in range(13):
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]
            dp[i][k]=dp[i][k]%mod
        else:
            number=int(s[i])
            for k in range(13):
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m
s=list(input())
mod=10**9+7
K=modinv(10,13)
U=[[0 for i in range(10) ]for k in range(13)]
for i in range(13):
    for j in range(10):
        U[i][j]=((i-j)*K)%13

dp=[[0 for k in range(13)] for i in range(len(s))]
#dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
num=s[0]
if s[0]=="?":
    for i in range(10):
        dp[0][i]=1
else:
    number=int(s[0])
    dp[0][number]=1

for i in range(1,len(s)):
    if s[i]=="?":
        for k in range(13):
            for j in range(10):
                dp[i][k]+=dp[i-1][U[k][j]]
        dp[i][k]=dp[i][k]%mod
    else:
        number=int(s[i])
        for k in range(13):
            dp[i][k]=dp[i-1][U[k][number]]%mod
print(dp[len(s)-1][5]%mod)


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Runtime Error):
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m
s=list(input())
mod=10**9+7
U=[[0 for i in range(10) ]for k in range(13)]
for i in range(13):
    for j in range(10):
        U[i][j]=((i-j)*K)%13
K=modinv(10,13)
dp=[[0 for k in range(13)] for i in range(len(s))]
#dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
num=s[0]
if s[0]=="?":
    for i in range(10):
        dp[0][i]=1
else:
    number=int(s[0])
    dp[0][number]=1

for i in range(1,len(s)):
    if s[i]=="?":
        for k in range(13):
            for j in range(10):
                dp[i][k]+=dp[i-1][U[k][j]]
        dp[i][k]=dp[i][k]%mod
    else:
        number=int(s[i])
        for k in range(13):
            dp[i][k]=dp[i-1][U[k][number]]%mod
print(dp[len(s)-1][5]%mod)


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m
S=input()
L=len(S)
s=[0 for i in range(L)]
for i in range(L):
    if S[i]=="?":
        s[i]=10
    else:
        s[i]=int(S[i])

mod=10**9+7
K=modinv(10,13)
dp=[[0 for k in range(13)] for i in range(L)]
#dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
num=s[0]
if s[0]==10:
    for i in range(10):
        dp[0][i]=1
else:
    number=s[0]
    dp[0][number]=1

for i in range(1,L):
    if s[i]==10:
        for k in range(13):
            for j in range(10):
                dp[i][k]+=dp[i-1][((k-j)*K)%13]
        dp[i][k]=dp[i][k]%mod
    else:
        number=s[i]
        for k in range(13):
            dp[i][k]=dp[i-1][((k-number)*K)%13]
print(dp[L-1][5]%mod)


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Runtime Error):
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m
S=input()
s=[0 for i in range(len(s))]
for i in range(len(s)):
    if S[i]=="?":
        s[i]=10
    else:
        s[i]=int(S[i])

mod=10**9+7
K=modinv(10,13)
dp=[[0 for k in range(13)] for i in range(len(s))]
#dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
num=s[0]
if s[0]==10:
    for i in range(10):
        dp[0][i]=1
else:
    number=s[0]
    dp[0][number]=1

for i in range(1,len(s)):
    if s[i]==10:
        for k in range(13):
            for j in range(10):
                dp[i][k]+=dp[i-1][((k-j)*K)%13]
        dp[i][k]=dp[i][k]%mod
    else:
        number=s[i]
        for k in range(13):
            dp[i][k]=dp[i-1][((k-number)*K)%13]
print(dp[len(s)-1][5]%mod)

Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m
s=list(input())
mod=10**9+7
K=modinv(10,13)
dp=[[0 for k in range(13)] for i in range(len(s))]
#dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
num=s[0]
if s[0]=="?":
    for i in range(10):
        dp[0][i]=1
else:
    number=int(s[0])
    dp[0][number]=1

for i in range(1,len(s)):
    if s[i]=="?":
        for k in range(13):
            for j in range(10):
                dp[i][k]+=dp[i-1][((k-j)*K)%13]
        dp[i][k]=dp[i][k]%mod
    else:
        number=int(s[i])
        for k in range(13):
            dp[i][k]=dp[i-1][((k-number)*K)%13]%mod
print(dp[len(s)-1][5]%mod)


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m
s=list(input())
mod=10**9+7
K=modinv(10,13)
dp=[[0 for k in range(13)] for i in range(len(s))]
#dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
num=s[0]
if s[0]=="?":
    for i in range(10):
        dp[0][i]=1
else:
    number=int(s[0])
    dp[0][number]=1

for i in range(1,len(s)):
    if s[i]=="?":
        for k in range(13):
            for j in range(10):
                dp[i][k]+=dp[i-1][((k-j)*K)%13]
        dp[i][k]=dp[i][k]%mod
    else:
        number=int(s[i])
        for k in range(13):
            dp[i][k]=dp[i-1][((k-number)*K)%13]%mod
print(dp[len(s)-1][5]%mod)

Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
s=input()
s=s[::-1]

n=len(s)
modlist=[[0 for i in range(13)]for _ in range(n+1)]

#13で割ったあまりの判定方法
if s[0]!="?":
    modlist[0][int(s[0])]=1
elif s[0]=="?":
    for  i in range(10):
        modlist[0][i]=1
for i in range(1,n):
    if s[i]!="?":
        add=(int(s[i])*(10**(i)))%13
        for  j in range(13):
            modlist[i][j]+=modlist[i-1][(j-add)%13]
            modlist[i][j]%(10**9+7)
            

    else:
        for nums in range(10):
                add=nums*(10**i)%13
                for  j in range(13):
                    modlist[i][j]+=modlist[i-1][(j-add)%13]
                    modlist[i][j]=modlist[i][j]%(10**9+7)

print(modlist[-2][5])                
            


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
s=input()
s=s[::-1]

n=len(s)
modlist=[[0 for i in range(13)]for _ in range(n+1)]

#13で割ったあまりの判定方法
if s[0]!="?":
    modlist[0][int(s[0])]=1
elif s[0]=="?":
    for  i in range(10):
        modlist[0][i]=1
for i in range(1,n):
    if s[i]!="?":
        add=(int(s[i])*(10**(i)))%13
        for  j in range(13):
            modlist[i][j]+=modlist[i-1][(j-add)%13]
            

    else:
        for nums in range(10):
                add=nums*(10**i)%13
                for  j in range(13):
                    modlist[i][j]+=modlist[i-1][(j-add)%13]
                   

print(modlist[-2][5]%(10**9+7))                
            


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
s=input()
s=s[::-1]

n=len(s)
modlist=[[0 for i in range(13)]for _ in range(n+1)]

#13で割ったあまりの判定方法
if s[0]!="?":
    modlist[0][int(s[0])]=1
elif s[0]=="?":
    for  i in range(10):
        modlist[0][i]=1
for i in range(1,n):
    if s[i]!="?":
        add=(int(s[i])*(10**(i)))%13
        for  j in range(13):
            modlist[i][j]+=modlist[i-1][(j-add)%13]
            modlist[i][j]%(10**9+7)
            

    else:
        for nums in range(10):
                add=nums*(10**i)%13
                for  j in range(13):
                    modlist[i][j]+=modlist[i-1][(j-add)%13]
                    modlist[i][j]=modlist[i][j]%(10**9+7)

print(modlist[-2][5])                
            

Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
s=input()
s=s[::-1]

n=len(s)
modlist=[[0 for i in range(13)]for _ in range(n+1)]

#13で割ったあまりの判定方法
if s[0]!="?":
    modlist[0][int(s[0])]=1
elif s[0]=="?":
    for  i in range(10):
        modlist[0][i]=1
for i in range(1,n):
    if s[i]!="?":
        add=(int(s[i])*(10**(i)))%13
        for  j in range(13):
            modlist[i][j]+=modlist[i-1][(j-add)%13]
            modlist[i][j]%(10**9+7)
            

    else:
        for nums in range(10):
                add=nums*(10**i)%13
                for  j in range(13):
                    modlist[i][j]+=modlist[i-1][(j-add)%13]
                    modlist[i][j]=modlist[i][j]%(10**9+7)

print(modlist[-2][5])                
            

Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0
def modinv(a, m):
    g, x, y = xgcd(a, m)
    return x % m
def main():
    s=list(input())
    mod=10**9+7
    K=modinv(10,13)
    U=[[0 for i in range(10) ]for k in range(13)]
    for i in range(13):
        for j in range(10):
            U[i][j]=((i-j)*K)%13

    dp=[[0 for k in range(13)] for i in range(len(s))]
    #dp[i][j]=初めのindex=i番目まで見たときに、あまりがjになるような方法の総数
    num=s[0]
    if s[0]=="?":
        for i in range(10):
            dp[0][i]=1
    else:
        number=int(s[0])
        dp[0][number]=1

    for i in range(1,len(s)):
        for k in range(13):
            if s[i]=="?":
                for j in range(10):
                    dp[i][k]+=dp[i-1][U[k][j]]%mod
            else:
                number=int(s[i])
                dp[i][k]=dp[i-1][U[k][number]]%mod
    print(dp[len(s)-1][5]%mod)
if __name__ == "__main__":
    main()