Buggy python submission (verdict: Time Limit Exceeded):
from sys import stdin
import numpy as np
def main():
    #入力
    readline=stdin.readline
    mod=10**9+7
    s=readline().strip()
    n=len(s)

    dp=np.zeros(13,dtype=np.int64)
    tmp1=np.arange(10,dtype=np.int64)
    keta=10
    for i in range(n-1,-1,-1):
        if i==n-1:
            if s[i]=="?":
                dp[0:10]=1
            else:
                dp[int(s[i])]=1
        else:
            if s[i]=="?":
                tmp2=(keta*tmp1)%13
            else:
                tmp2=(keta*int(s[i]))%13
            nex=np.zeros(13,dtype=np.int64)
            for j in range(13):
                nex[(tmp2+j)%13]+=dp[j]
            nex%=mod
            dp=nex
            keta*=10
            keta%=13

    print(dp[5])

if __name__=="__main__":
    main()

Fixed submission:
#import numpy as np
def main():
    S=input()
    #dp=np.zeros((len(S)+1,13),dtype=int)
    dp=[[0]*13 for _ in range(len(S)+1)]
    dp[0][0]=1
    mod=10**9+7
    """
    for i in range(1,len(S)+1):
        for a in range(13):
            if S[i-1]=="?":
                if a*10%13<(a*10+10)%13:
                    dp[i][a*10%13:(a*10+10)%13]+=dp[i-1][a]
                    dp[i][a*10%13:(a*10+10)%13]%=mod
                else:
                    dp[i][a*10%13:]+=dp[i-1][a]
                    dp[i][a*10%13:]%=mod
                    dp[i][:(a*10+10)%13]+=dp[i-1][a]
                    dp[i][:(a*10+10)%13]%=mod
            else:
                dp[i][(a*10+int(S[i-1]))%13]+=dp[i-1][a]
                dp[i][(a*10+int(S[i-1]))%13]%=mod
    print(dp[len(S)][5])
"""
    for i in range(1,len(S)+1):
        for a in range(13):
            if S[i-1]=="?":
                for n in range(10):
                    dp[i][(a*10+n)%13]+=dp[i-1][a]
                    dp[i][(a*10+n)%13]%=mod
            else:
                dp[i][(a*10+int(S[i-1]))%13]+=dp[i-1][a]
                dp[i][(a*10+int(S[i-1]))%13]%=mod
    print(dp[len(S)][5])
if __name__=="__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
from sys import stdin
import numpy as np
def main():
    #入力
    readline=stdin.readline
    mod=10**9+7
    s=readline().strip()
    n=len(s)

    dp=np.zeros((n,13),dtype=np.int64)
    tmp1=np.array(range(10),dtype=np.int64)%13
    keta=10
    for i in range(n-1,-1,-1):
        if i==n-1:
            if s[i]=="?":
                dp[i,0:10]=1
            else:
                dp[i][int(s[i])]=1
        else:
            if s[i]=="?":
                tmp2=(keta*tmp1)%13
            else:
                tmp2=(keta*int(s[i]))%13
            for j in range(13):
                dp[i,(tmp2+j)%13]+=dp[i+1,j]
            dp[i]%=mod
            keta*=10
            keta%=13

    print(dp[0][5])

if __name__=="__main__":
    main()

Fixed submission:
#import numpy as np
def main():
    S=input()
    #dp=np.zeros((len(S)+1,13),dtype=int)
    dp=[[0]*13 for _ in range(len(S)+1)]
    dp[0][0]=1
    mod=10**9+7
    """
    for i in range(1,len(S)+1):
        for a in range(13):
            if S[i-1]=="?":
                if a*10%13<(a*10+10)%13:
                    dp[i][a*10%13:(a*10+10)%13]+=dp[i-1][a]
                    dp[i][a*10%13:(a*10+10)%13]%=mod
                else:
                    dp[i][a*10%13:]+=dp[i-1][a]
                    dp[i][a*10%13:]%=mod
                    dp[i][:(a*10+10)%13]+=dp[i-1][a]
                    dp[i][:(a*10+10)%13]%=mod
            else:
                dp[i][(a*10+int(S[i-1]))%13]+=dp[i-1][a]
                dp[i][(a*10+int(S[i-1]))%13]%=mod
    print(dp[len(S)][5])
"""
    for i in range(1,len(S)+1):
        for a in range(13):
            if S[i-1]=="?":
                for n in range(10):
                    dp[i][(a*10+n)%13]+=dp[i-1][a]
                    dp[i][(a*10+n)%13]%=mod
            else:
                dp[i][(a*10+int(S[i-1]))%13]+=dp[i-1][a]
                dp[i][(a*10+int(S[i-1]))%13]%=mod
    print(dp[len(S)][5])
if __name__=="__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
from sys import stdin
import numpy as np
def main():
    #入力
    readline=stdin.readline
    mod=10**9+7
    s=readline().strip()
    n=len(s)

    dp=np.zeros((n,13),dtype=np.int64)
    tmp1=np.array(range(10),dtype=np.int64)%13
    keta=10
    for i in range(n-1,-1,-1):
        if i==n-1:
            if s[i]=="?":
                dp[i,0:10]=1
            else:
                dp[i][int(s[i])]=1
        else:
            if s[i]=="?":
                tmp2=(keta*tmp1)%13
            else:
                tmp2=(keta*int(s[i]))%13
            for j in range(13):
                dp[i][(tmp2+j)%13]+=dp[i+1][j]
            dp[i]%=mod
            keta*=10
            keta%=13

    print(dp[0][5])

if __name__=="__main__":
    main()

Fixed submission:
#import numpy as np
def main():
    S=input()
    #dp=np.zeros((len(S)+1,13),dtype=int)
    dp=[[0]*13 for _ in range(len(S)+1)]
    dp[0][0]=1
    mod=10**9+7
    """
    for i in range(1,len(S)+1):
        for a in range(13):
            if S[i-1]=="?":
                if a*10%13<(a*10+10)%13:
                    dp[i][a*10%13:(a*10+10)%13]+=dp[i-1][a]
                    dp[i][a*10%13:(a*10+10)%13]%=mod
                else:
                    dp[i][a*10%13:]+=dp[i-1][a]
                    dp[i][a*10%13:]%=mod
                    dp[i][:(a*10+10)%13]+=dp[i-1][a]
                    dp[i][:(a*10+10)%13]%=mod
            else:
                dp[i][(a*10+int(S[i-1]))%13]+=dp[i-1][a]
                dp[i][(a*10+int(S[i-1]))%13]%=mod
    print(dp[len(S)][5])
"""
    for i in range(1,len(S)+1):
        for a in range(13):
            if S[i-1]=="?":
                for n in range(10):
                    dp[i][(a*10+n)%13]+=dp[i-1][a]
                    dp[i][(a*10+n)%13]%=mod
            else:
                dp[i][(a*10+int(S[i-1]))%13]+=dp[i-1][a]
                dp[i][(a*10+int(S[i-1]))%13]%=mod
    print(dp[len(S)][5])
if __name__=="__main__":
    main()

Buggy python submission (verdict: Time Limit Exceeded):
import numpy as np
def main():
    S=input()
    dp=np.zeros((len(S)+1,13),dtype=int)
    dp[0][0]=1
    mod=10**9+7
    for i in range(1,len(S)+1):
        for a in range(13):
            if S[i-1]=="?":
                if a*10%13<(a*10+10)%13:
                    dp[i][a*10%13:(a*10+10)%13]+=dp[i-1][a]
                    dp[i][a*10%13:(a*10+10)%13]%=mod
                else:
                    dp[i][a*10%13:]+=dp[i-1][a]
                    dp[i][a*10%13:]%=mod
                    dp[i][:(a*10+10)%13]+=dp[i-1][a]
                    dp[i][:(a*10+10)%13]%=mod
            else:
                dp[i][(a*10+int(S[i-1]))%13]+=dp[i-1][a]
                dp[i][(a*10+int(S[i-1]))%13]%=mod
    print(dp[len(S)][5])
"""
    for i in range(1,len(S)+1):
        for a in range(13):
            if S[i-1]=="?":
                for n in range(10):
                    dp[i][(a*10+n)%13]+=dp[i-1][a]
            else:
                dp[i][(a*10+int(S[i-1]))%13]+=dp[i-1][a]
"""
if __name__=="__main__":
    main()

Fixed submission:
#import numpy as np
def main():
    S=input()
    #dp=np.zeros((len(S)+1,13),dtype=int)
    dp=[[0]*13 for _ in range(len(S)+1)]
    dp[0][0]=1
    mod=10**9+7
    """
    for i in range(1,len(S)+1):
        for a in range(13):
            if S[i-1]=="?":
                if a*10%13<(a*10+10)%13:
                    dp[i][a*10%13:(a*10+10)%13]+=dp[i-1][a]
                    dp[i][a*10%13:(a*10+10)%13]%=mod
                else:
                    dp[i][a*10%13:]+=dp[i-1][a]
                    dp[i][a*10%13:]%=mod
                    dp[i][:(a*10+10)%13]+=dp[i-1][a]
                    dp[i][:(a*10+10)%13]%=mod
            else:
                dp[i][(a*10+int(S[i-1]))%13]+=dp[i-1][a]
                dp[i][(a*10+int(S[i-1]))%13]%=mod
    print(dp[len(S)][5])
"""
    for i in range(1,len(S)+1):
        for a in range(13):
            if S[i-1]=="?":
                for n in range(10):
                    dp[i][(a*10+n)%13]+=dp[i-1][a]
                    dp[i][(a*10+n)%13]%=mod
            else:
                dp[i][(a*10+int(S[i-1]))%13]+=dp[i-1][a]
                dp[i][(a*10+int(S[i-1]))%13]%=mod
    print(dp[len(S)][5])
if __name__=="__main__":
    main()