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: Wrong Answer)

import numpy as np
MOD = 10 ** 9 + 7

dp = np.zeros(13, dtype = np.int64)
dp[0] = 1

move = np.arange(0,52,4) % 13
for s in input():
  prev = dp#[move]
  dp = np.zeros(13, dtype=np.int64)
  if s == '?':
    add = range(10)
  else:
    add = [int(s)]
  for x in add:
    dp[x:13] += prev[:13-x]
    dp[0:x] += prev[13-x:13]
  dp %= MOD
  
print(dp[5])