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 (1.14.1) (judge verdict: Time Limit Exceeded)

package main

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

const Mod = int(1e9) + 7

func main() {
	S := ReadString()
	dp := make([][]int, len(S)+1)
	for i := 0; i < len(S)+1; i++ {
		dp[i] = make([]int, 13)
	}
	dp[0][0] = 1
	for i := 0; i < len(S); i++ {
		for r := 0; r < 13; r++ {
			base := 1
			for k := 0; k < len(S)-i-1; k++ {
				base *= 10
				base %= 13
			}
			if S[i] == '?' {
				for x := 0; x <= 9; x++ {
					prev := (13 + (r-base*x)%13) % 13
					dp[i+1][r] += dp[i][prev]
					dp[i+1][r] %= Mod
				}
			} else {
				x := int(S[i] - '0')
				prev := (13 + (r-base*x)%13) % 13
				dp[i+1][r] += dp[i][prev]
			}
		}
	}
	fmt.Println(dp[len(S)][5])
}

var reader = bufio.NewReader(os.Stdin)

func Scan(a ...interface{}) {
	if _, err := fmt.Fscan(reader, a...); err != nil {
		panic(err)
	}
}
func ReadInt() (i int)       { Scan(&i); return }
func ReadString() (s string) { Scan(&s); return }
func ReadInts(n int) []int {
	v := make([]int, n)
	for i := 0; i < n; i++ {
		Scan(&v[i])
	}
	return v
}