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: Accepted)

M = 10 ** 9 + 7
s = gets().strip()

num = 0
q_list = []
d = 1

s.each_char.reverse_each{|c|
	if c != "?"
		num = (num + c.to_i() * d) % 13
	else
		q_list << d
	end
	d = (d * 10) % 13
}

counts = [0] * 13
counts[0] = 1
counts_save = [0] * 13
q_list.each{|d|
	13.times{|i|
		counts_save[i] = counts[i] % M
	}
	(1...10).each{|n|
		r = (d * n) % 13
		13.times{|m|
			counts[(r + m) % 13] += counts_save[m]
		}
	}
}

puts(counts[(13 + 5 - num) % 13] % M)