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 (2.7.6) (judge verdict: Accepted)

#abc135d
s=raw_input()
mod=10**9+7
res=[0]*13
res[0]=1
for i in s:
 dp=[0]*13
 for j in range(13):
  dp[(j*10)%13]=res[j]%mod
 dp+=dp
 if i=='?':
  for k in range(13):
   res[k]=sum(dp[k+4:k+14])
 else:
  for k in range(13):
   res[k]=dp[k+13-int(i)]
print res[5]%mod