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: Wrong Answer)

package main

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

var sc *bufio.Scanner

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

const MOD = 1000000007
const DIV = 13
const BASE = 10

func main() {
	sc = bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	sc.Scan()
	rs := append([]rune{'0'}, []rune(sc.Text())...)
	n := len(rs) - 1

	dp := make([][]int, n+1)
	for i := range dp {
		dp[i] = make([]int, DIV)
	}
	dp[0][0] = 1

	for i := 1; i <= n; i++ {
		var digit int
		switch {
		case rs[i] == '?':
			digit = -1
		default:
			digit = int(rs[i] - '0')
		}

		for j := 0; j < BASE; j++ {
			if digit != -1 && digit != j {
				continue
			}
			for k := 0; k < DIV; k++ {
				dp[i][(k*BASE+j)%DIV] = (dp[i][(k*BASE+j)%DIV] + dp[i-1][k]) % MOD
			}
		}
	}
	fmt.Println(dp[n][5])
}