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: Time Limit Exceeded)

def main():
  s = input()
  divisor = 10 ** 9 + 7
  lut = [i % 13 for i in range(133)]
  dp = [[0] * 13 for _ in range(len(s) + 1)]
  dp[0][0] = 1
  list10 = list(range(10))
  list13 = list(range(13))
  for i in range(len(s)):
    dpi = dp[i]
    dpi1 = dp[i + 1]
    if s[i] == '?':
      for j in list10:
        m = j
        for k in list13:
          dpi1[m] += dpi[k]
          m = lut[m + 10]
    else:
      m = int(s[i])
      for k in list13:
        dpi1[m] += dpi[k]
        m = lut[m + 10]
    for k in range(13):
      dpi1[k] %= divisor
  print(dp[len(s)][5])
main()