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 Julia (0.5.0) (judge verdict: Time Limit Exceeded)

parseInt(x)=parse(Int,x)
parseMap(x::Array{SubString{String},1})=map(parseInt,x)

function main()
	mod = 1000000007
	s = readline() |> chomp
	g = zeros(Int,13,13)
	for i in 0:12
		for j in 0:12
			g[i+1,j+1] = (10*i+j)%13
		end
	end
	dp = zeros(Int,length(s),13)
	if s[1] == '?'
		for i in 1:10
			dp[1,i] = 1
		end
	else
		dp[1,parseInt(s[1:1])+1] = 1
	end
	for i in 2:length(s)
		if s[i] == '?'
			for j in 1:13
				for k in 1:10
					x = g[j,k]+1
					dp[i,x] = (dp[i,x]+dp[i-1,j])%mod
				end
			end
		else
			for j in 1:13
				x = g[j,parseInt(s[i:i])+1]+1
				dp[i,x] = (dp[i,x]+dp[i-1,j])%mod
			end
		end
	end
	println(dp[length(s),6])
end

main()