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: Time Limit Exceeded)

package main

import (
	"fmt"
	"io"
	"os"
	"strconv"
	"strings"
)

func proc(r io.Reader, w io.Writer) {
	const bignum = 1000000007
	var s string
	fmt.Fscanf(r, "%s", &s)
	width := len(s)
	format := fmt.Sprintf("%%0%dd", width)
	maxNumber, _ := strconv.Atoi(strings.Replace(s, "?", "9", -1))
	minNumber, _ := strconv.Atoi(strings.Replace(s, "?", "0", -1))

	max := (maxNumber - 5) / 13
	min := (minNumber + 13 - 5 - 1) / 13
	cnt := 0
	for i := min; i <= max; i++ {
		number := i*13 + 5
		t := fmt.Sprintf(format, number)
		ok := true
		for j, c := range s {
			if c == '?' {
				continue
			}
			if c != rune(t[j]) {
				ok = false
				break
			}
		}
		if ok {
			cnt++
			if cnt > bignum {
				cnt -= bignum
			}
		}
	}
	//fmt.Printf("%#v", numbers)
	fmt.Fprintf(w, "%d", cnt)
}

func main() {
	proc(os.Stdin, os.Stdout)
}