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"
)

const MOD = 1000000007

func main() {
	var s string
	fmt.Scan(&s)
	
	n := len(s)
	dp := make([][]int, n)
	for i := 0; i < n; i++ {
		dp[i] = make([]int, 13)
	}

	if s[n-1] == '?' {
		for i := 0; i < 13; i++ {
			if i < 10 {
				dp[n-1][i] = 1
			} else {
				dp[n-1][i] = 0
			}
		}
	} else {
		c := int(s[n-1] - '0')
		for i := 0; i < 13; i++ {
			if i == c {
				dp[n-1][i] = 1
			} else {
				dp[n-1][i] = 0
			}
		}
	}
	
	digit := 10
	for i := n - 2; i >= 0; i-- {
		if s[i] == '?' {
			for m := 0; m < 10; m++ {
				for mod, cnt := range dp[i+1] {
					shifted := (mod + m * digit) % 13
					dp[i][shifted] += cnt
				}
			}
		} else {
			m := int(s[i] - '0')
			for mod, cnt := range dp[i+1] {
				shifted := (mod + m * digit) % 13
				dp[i][shifted] += cnt
			}
		}
		
		for j := 0; j < 13; j++ {
			dp[i][j] %= MOD
		}
		digit = (digit * 10) % 13
	}

	fmt.Println(dp[0][5])
}