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 Ruby (2.3.3) (judge verdict: Wrong Answer)

S=gets.chomp
MOD=10**9+7
dp=[0]*13
dp[0]=1
bias=1
(S.size-1).downto(0){|i|
  ndp=[0]*13
  13.times{|m|
    if S[i]=="?" then
      10.times{|j|
        ndp[(m+j*bias)%13]+=dp[m]
      }
		else
      ndp[(m+(S[i].to_i)*bias)%13]+=dp[m]
	  end
  }
  dp=ndp.map{|x|x%MOD}
  p dp
  bias*=10
  if bias.abs>999 then bias*=-1/1000 end
}
p dp[5]