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: Runtime Error)

fun main(argc:Array<String>){
    val MOD = 1000000007L;

    val S = readLine()!!
    var dp = Array(10005, {i->Array(13, {i->0L})})
    dp[0][0] = 1

    for (i in 0..S.length-1){
        var c = 0
        if (S[i] == '?') {
            c = -1
        }
        else {
            c = S[i].toString().toInt()
        }

        for (j in 0..9){
            if (c != -1 && c != j){
                continue
            }
            for (ki in 0..12){
                dp[i+1][(ki*10+j) % 13] += dp[i][ki]
            }
        }
        for (j in 1..12){
            dp[i+1][j] %= MOD
        }
    }
  
    println(dp[S.length][5])
}