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)

import numpy as np
s=list(input())
n=len(s)
dp=np.zeros((n+1,13),np.int64)
mod=pow(10,9)+7
if s[-1]=='?':
  dp[1][:10]=1
else:
  dp[1][int(s[-1])]=1
for i in range(2,n+1):
  if s[-i]=='?':
    for j in range(10):
      if (j*pow(10,i-1))%13==0:
        dp[i]+=dp[i-1]
      else:
        dp[i][(j*pow(10,i-1))%13:]+=dp[i-1][:-(j*pow(10,i-1))%13]
        dp[i][:(j*pow(10,i-1))%13]+=dp[i-1][-(j*pow(10,i-1))%13:]
  else:
    j=int(s[-i])
    if (j*pow(10,i-1))%13==0:
      dp[i]+=dp[i-1]
    else:
      dp[i][(j*pow(10,i-1))%13:]+=dp[i-1][:-(j*pow(10,i-1))%13]
      dp[i][:(j*pow(10,i-1))%13]+=dp[i-1][-(j*pow(10,i-1))%13:]
  dp[i]%=mod
print(dp[n][5])
#print(dp)