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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
	val MOD : Long = java.lang.Math.pow(10.0, 9.0).toLong() + 7

	var s = readLine()!!.trim().toCharArray().map{ x -> x.toString() }

	var dp = Array(13) { 0L }
	dp[0] = 1L

	for (i in (0 .. (s.size - 1) )) {
		var dp_next = Array(13) { 0L }
	
		if (s[i] == "?") {
			for (j in 0..12){
				for (k in 0..9){
					dp_next[(j * 10 + k) % 13] += dp[j]
				}
			}
		} else {
			for (j in 0..12){
				dp_next[(j * 10 + s[i].toInt()) % 13] += dp[j]
			}
		}

		for (j in 0..12){
			if (dp_next[j] > MOD) {
				dp_next[j] = dp_next[j] % MOD
			}
		}
		
		dp = dp_next
	}

	println(dp[5] % MOD)
}