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"

func main()  {
	var s string
	fmt.Scan(&s)

	const N int32 = 13
	dp := make([]int32, N)
	dp[0] = 1

	var c byte
	mul := int32(1)
	for i := len(s)-1; i>=0; i-- {
		nextDP := make([]int32, N)
		mod := int32(1000000007)
		c = s[i]
		if c == '?' {
			for k := int32(0); k < 10; k++ {
				for j := int32(0); j < N; j++ {
					nextDP[(k*mul+ j)%N] += dp[j]
					nextDP[(k*mul+ j)%N] %= mod
				}
			}
		} else {
			k := int32(s[i] - '0')
			for j := int32(0); j < N; j++ {
				nextDP[(k*mul+ j)%N] += dp[j]
				nextDP[(k*mul+ j)%N] %= mod
			}
		}
		mul *= 10
		mul %= N
		dp = nextDP
	}
	fmt.Println(dp[5])
}