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)

s=input()
n=len(s)
DP=[[0]*13 for _ in range(n+1)]
DP[0][0]=1
for i in range(n):
  r=(10**(n-1-i))%13
  if s[i]=="?":
    for j in range(10):
      rr=(r*j)%13
      for k in range(13):
        if k>=rr:
          DP[i+1][k]+=DP[i][k-rr]
        else:
          DP[i+1][k]+=DP[i][k-rr+13]
  else:
    rr=(r*int(s[i]))%13
    for k in range(13):
      if k>=rr:
        DP[i+1][k]+=DP[i][k-rr]
      else:
        DP[i+1][k]+=DP[i][k-rr+13]
print(DP[n][5]%(10**9+7))