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 Python (3.4.3) (judge verdict: Runtime Error)

S = list(input())
N = len(S)
dp = [ [0 for i in range(13)] for i in range(N+1)]
keta = 0.1
mod = 10**9 + 7

S.reverse()

for i in range(1,N+1):
  
  amaarr = [0 for ii in range(13)]
  c = S[i-1]
  keta *= 10 % mod
  if c == "?":
    for j in range(10):
      amari = int( keta * j % 13 )
      amaarr[amari] += 1
  else:
    amari = int( keta * int(c) % 13 )
    amaarr[amari] += 1
    
  if i == 1:
    for k in range(13):
      am = amaarr[k]
      dp[i][k] += am
      
  else:
    for k in range(13):
      am = amaarr[k]
      for l in range(13):
        dp[i][(l+k)%13] += dp[i-1][l] * am  % mod

         
print(dp[-1][5])