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: Time Limit Exceeded)

#input of int(split by space)
def get_i()
  return gets.chomp.split(" ").map(&:to_i)
end
#input of float(split by space)
def get_f()
  return gets.chomp.split(" ").map(&:to_f)
end
#input of string(split by space)
def get()
  return gets.chomp.split(" ")
end
#input of string(split per one character)
def get_nsp()
  return gets.chomp.split("")
end
#yes or no decision
def yn_judge(bool,y="Yes",n="No")
  return bool ? y : n 
end
#create of array
def array(size1,init=nil,size2=-1)
  if size2==-1
    return Array.new(size1){init}
  else
    return Array.new(size2){Array.new(size1){init}}
  end
end

def max(a,b)
    return a>b ? a : b
end

def min(a,b)
    return a>b ? b : a
end

INF=Float::INFINITY

MOD=10**9+7
S=get_nsp.reverse
#S=["?"]*(10**5)
L=S.size
dp=Array.new(13){0}
dp[0]=1
b=1
S.each_with_index do|s,i|
    dp2=Array.new(13){0}
    if s!="?"
        t=s.to_i*b
        13.times do|k|
            dp2[(k+t)%13]+=dp[k]
            dp2[k]%=MOD
        end
    else
        13.times do|k|
            t=0
            10.times do|d|
                dp2[(k+t)%13]+=dp[k]
                t+=b
            end
            dp2[k]%=MOD
        end
    end
        #13.times do|k|
          #if s!="?"
              #dp2[(k+s.to_i*b)%13]+=dp[k]
          #else
            #10.times do|d|
                #dp2[(k+d*b)%13]+=dp[k]
            #end
          #end
          #dp2[k]%=MOD
        #end
    dp=dp2
    b*=10
    b%=13
end
puts dp[5]%MOD