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)

mod=10**9+7
s=input()
dp=[[0]*13 for _ in range(len(s)+1)]
dp[0][0]=1
r=[i%13 for i in range(130)]

for i in range(len(s)):
  if s[i]=='?':
    for j in range(13):
      for k in range(10):
        dp[i+1][r[j*10+k]]+=dp[i][j]
  else:
    t = int(s[i])
    for j in range(13):
      dp[i+1][r[j*10+t]] += dp[i][j]

  for k in range(13):
    dp[i+1][k] %= mod

print(dp[len(s)][5])