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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
	"strconv"
)

const mod = 1e9 + 7

func min(x, y int) int {
	if x < y {
		return x
	}
	return y
}

func main() {
	var s string
	fmt.Scan(&s)
	l := len(s)
	a := [13]int{}
	a[0] = 1
	for j := 0; j < l; j++ {
		b := [13]int{}
		k := s[j : j+1]
		if k == "?" {
			for o := 0; o < 13; o++ {
				ai := a[o]
				ii := o * 10 % 13
				for m := 0; m < 10; m++ {
					b[(ii+m)%13] += ai
				}
			}
			for o := 0; o < 13; o++ {
				b[o] %= mod
			}
		} else {
			tt, _ := strconv.ParseInt(k, 10, 64)
			t := int(tt)
			for o := 0; o < 13; o++ {
				ai := a[o]
				ii := (o*10 + t) % 13
				b[ii] = ai
			}
		}
		a = b
	}
	fmt.Println(a[5])
}