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"
)

const (
	mod = int(1e9 + 7)
)

func main() {
	input := bufio.NewReader(os.Stdin)

	var S string
	fmt.Fscanf(input, "%s\n", &S)

	dp := make([][]int, 100001)
	for i := range dp {
		dp[i] = make([]int, 13)
	}

	dp[0][0] = 1
	for i := range S {
		if S[i] == '?' {
			for d := 0; d < 10; d++ {
				for j := 0; j < 13; j++ {
					dp[i+1][(j*10+d)%13] += dp[i][j]
				}
			}
		} else {
			d := int(S[i] - '0')
			for j := 0; j < 13; j++ {
				dp[i+1][(j*10+d)%13] += dp[i][j]
			}
		}
		for j := 0; j < 13; j++ {
			dp[i+1][j] %= mod
		}
	}
	fmt.Println(dp[len(S)][5])
}