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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func nextInt() int {
	sc.Scan()
	i, e := strconv.Atoi(sc.Text())
	if e != nil {
		panic(e)
	}
	return i
}

func nextLine() string {
	sc.Scan()
	return sc.Text()
}

const MOD = 1000000007

var dp [100005][13]int
var n int

func main() {
	var s string

	fmt.Scan(&s)
	n := len(s)

	dp[0][0] = 1
	for i := 0; i < n; i++ {
		var c int
		if s[i] == '?' {
			c = -1
		} else {
			c = int(s[i] - '0')
		}

		for j := 0; j < 10; j++ {
			if c != -1 && c != j {
				continue
			}
			for ki := 0; ki < 13; ki++ {
				dp[i+1][(ki*10+j)%13] += dp[i][ki]
			}
		}

		for j := 0; j < 13; j++ {
			dp[i+1][j] %= MOD
		}
	}
	res := dp[n][5]

	fmt.Println(res)
}