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: Wrong Answer)

S = input()
L = len(S)
V = [[0] * 13 for i in range(L)]
A = 0
flag = True

for i in range(L):
  if S[L-i-1] != '?':
    A += 10 ** i * int(S[L-i-1]) % 13
A = A % 13


for i in range(L):
  
  for j in range(13):
    V[i][j] = V[i-1][j]
  
  if S[L-i-1] == '?':
    
    if flag:
      for j in range(10):
        k = j * pow(10, i) % 13
        V[i][k%13] += 1
      flag = False
        
    else:
      for j in range(1, 10):
        k = j * pow(10, i) % 13
        for m in range(13):
          V[i][(m+k)%13] += V[i-1][m]

print(V[-1][(18-A)%13]% (10 ** 9 + 7))