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 = '?'*100000#gets.chomp

ks, l = [12,3,4,1,10,9], []
ks.each{|k|
	l[k] = a = Array.new(13){ [] }
	js = [*0..12]
	9.times{
		js.rotate! k
		js.each_with_index{|j,i|
			a[i] << j
		}
	}
}
ks = ks.cycle

m = [1]+[0]*12
S.each_char.reverse_each.with_index{|c,i|
	k = ks.next
	if c != ??
		m.rotate! (c.ord-?0.ord)*k
	else
		m = l[k].map.with_index{|a,i|
			m.values_at(*a).inject(m[i],:+) % 1000000007
		}
	end
}
p m[5]