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"
	"io"
	"os"
	"strconv"
)

var (
	readString func() string
	readBytes  func() []byte
)

func init() {
	readString, readBytes = newReadString(os.Stdin)
}

func newReadString(ior io.Reader) (func() string, func() []byte) {
	r := bufio.NewScanner(ior)
	r.Buffer(make([]byte, 1024), int(1e+11))
	r.Split(bufio.ScanWords)

	f1 := func() string {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Text()
	}
	f2 := func() []byte {
		if !r.Scan() {
			panic("Scan failed")
		}
		return r.Bytes()
	}
	return f1, f2
}

func readInt() int {
	return int(readInt64())
}

func readInt64() int64 {
	i, err := strconv.ParseInt(readString(), 10, 64)
	if err != nil {
		panic(err.Error())
	}
	return i
}

func readFloat64() float64 {
	f, err := strconv.ParseFloat(readString(), 64)
	if err != nil {
		panic(err.Error())
	}
	return f
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func minInt64(a, b int64) int64 {
	if a < b {
		return a
	}
	return b
}

func maxInt64(a, b int64) int64 {
	if a > b {
		return a
	}
	return b
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

func absInt64(a int64) int64 {
	if a < 0 {
		return -a
	}
	return a
}

func sum(a []int) int {
	var ret int
	for i := range a {
		ret += a[i]
	}
	return ret
}

func sumInt64(a []int64) int64 {
	var ret int64
	for i := range a {
		ret += a[i]
	}
	return ret
}

func sumFloat64(a []float64) float64 {
	var ret float64
	for i := range a {
		ret += a[i]
	}
	return ret
}

func gcdInt64(m, n int64) int64 {
	for m%n != 0 {
		m, n = n, m%n
	}
	return n
}

func lcmInt64(m, n int64) int64 {
	return m / gcdInt64(m, n) * n
}

// sort ------------------------------------------------------------

type int64Array []int64

func (s int64Array) Len() int           { return len(s) }
func (s int64Array) Swap(i, j int)      { s[i], s[j] = s[j], s[i] }
func (s int64Array) Less(i, j int) bool { return s[i] < s[j] }

type xxx struct {
	x int
}

type sortArray []xxx

func (s sortArray) Len() int           { return len(s) }
func (s sortArray) Swap(i, j int)      { s[i], s[j] = s[j], s[i] }
func (s sortArray) Less(i, j int) bool { return s[i].x < s[j].x }

// -----------------------------------------------------------------

const mod int = 1e9 + 7

func main() {
	s := readString()
	n := len(s)

	dp := make([][]int, n+1)
	for i := range dp {
		dp[i] = make([]int, 13)
	}
	dp[0][0] = 1

	for i := 1; i < n+1; i++ {
		c := s[i-1 : i]
		cnum, _ := strconv.Atoi(c)
		for j := 0; j < 10; j++ {
			if c != "?" && j != cnum {
				continue
			}
			for k := 0; k < 13; k++ {
				dp[i][(k*10+j)%13] = (dp[i][(k*10+j)%13] + dp[i-1][k]) % mod
			}
		}
	}

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