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)

n = gets.chomp.split("").reverse
dp = Array.new(13,0)
dp[0]=1
nextdp = Array.new(13,0)
modmap=[9,12,3,4,1,10]
n.each_with_index{|ni, keta|
if keta==0 then
    need = 1
elsif keta==1 then
    need = 3
else
    need = modmap[(keta-2)%6]
end
nextdp=Array.new(13,0)
if ni == "?" then
    10.times{|n|
        mod = (n* need)%13
        13.times{|t|
            nextdp[(mod+t)%13] += dp[t]
            nextdp[(mod+t)%13] %= 1000000007
        }
    }
else
    mod = (ni.to_i * need)%13
    13.times{|t|
        nextdp[(mod+t)%13] += dp[t]
        nextdp[(mod+t)%13] %= 1000000007
    }
end
dp = nextdp
}
puts dp[5]