Problem:
Score : 400 points

Problem Statement

Given is a string S. Each character in S is either a digit (0, ..., 9) or ?.

Among the integers obtained by replacing each occurrence of ? with a digit, how many have a remainder of 5 when divided by 13? An integer may begin with 0.

Since the answer can be enormous, print the count modulo 10^9+7.

Constraints

S is a string consisting of digits (0, ..., 9) and ?.

1 \leq |S| \leq 10^5

Input

Input is given from Standard Input in the following format:

S

Output

Print the number of integers satisfying the condition, modulo 10^9+7.

Sample Input 1

??2??5

Sample Output 1

768

For example, 482305, 002865, and 972665 satisfy the condition.

Sample Input 2

?44

Sample Output 2

1

Only 044 satisfies the condition.

Sample Input 3

7?4

Sample Output 3

0

We may not be able to produce an integer satisfying the condition.

Sample Input 4

?6?42???8??2??06243????9??3???7258??5??7???????774????4?1??17???9?5?70???76???

Sample Output 4

153716888

Solution in PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
from collections import Counter, deque
#from collections import defaultdict
from itertools import combinations, permutations, accumulate, groupby, product
from bisect import bisect_left,bisect_right
from heapq import heapify, heappop, heappush
from math import floor, ceil,pi
#from operator import itemgetter
def I(): return int(input())
def MI(): return map(int, input().split())
def LI(): return list(map(int, input().split()))
def LI2(): return [int(input()) for i in range(n)]
def MXI(): return [LI()for i in range(n)]
inf = 10**17
mod = 10**9 + 7

s=input().rstrip()
l=len(s)
dp=[[0 for i in range(13)] for i in  range(l)]
#dp[0]=[1 for i in range(13)]
i=0
u=s[0]
if u!="?":
    k=(int(u)*10**(l-1))%13
    dp[0][k]+=1
else:
    for g in range(10):
        k=(g*10**(l-1))%13
        dp[0][k]+=1
#print(dp)
for i in range(l-1):
    u=s[i+1]
    t=(10**(l-i-2))%13
    for j in range(13):
        if u!="?":
            k=(j+int(u)*t)%13
            dp[i+1][k]+=dp[i][j]
        
        else:
            for g in range(10):
                k=(j+g*t)%13
                dp[i+1][k]+=dp[i][j]
    for d in dp[i+1]:
        d%=mod
                
            
#print(dp)
print(dp[l-1][5]%mod)