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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <bits/stdc++.h>
#include <cassert>
#include <climits>
#include <bitset>
#include <stack>
#include <iomanip>
#include <limits>
#include <string>
#include <cmath>
#include <math.h>
#include <algorithm>
#include <string.h>
#include <tuple>
#include <time.h>
#include <random>
#include <unistd.h>

using namespace std;

typedef long long ll;
typedef pair<ll,ll> P;

long long int INF = 1e18;
double Pi = 3.1415926535897932384626;

vector<ll> G[500005];
//vector<P> tree[500010];
priority_queue <ll> pql;
priority_queue <P> pqp;
//big priority queue
priority_queue <ll,vector<ll>,greater<ll> > pqls;
priority_queue <P,vector<P>,greater<P> > pqps;
//small priority queue
//top pop

int dx[8]={1,0,-1,0,1,1,-1,-1};
int dy[8]={0,1,0,-1,1,-1,-1,1};
char dir[] = "DRUL";
//ll bit[500005];
//↓,→,↑,←


#define p(x) cout<<x<<endl;
#define el cout<<endl;
#define pe(x) cout<<(x)<<" ";
#define ps(x) cout<<fixed<<setprecision(25)<<x<<endl;
#define pu(x) cout<<(x);
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define line cout << "----------" << endl;


ll mod = 1000000007;
ll rui(ll number1,ll number2){

    if(number2 == 0){
        return 1;
    }else{
        ll number3 = rui(number1,number2 / 2);
        number3 *= number3;
        number3 %= mod;
        if(number2%2==1){
            number3 *= number1;
            number3 %= mod;
        }
        return number3;
    }
}
ll gcd(ll number1,ll number2){

    if(number1 > number2){
        swap(number1,number2);
    }
    if(number1 == 0 || number1 == number2){
        return number2;
    }else{
        return gcd(number2 % number1,number1);
    }
}
void YES(bool condition){

    if(condition){
        p("YES");
    }else{
        p("NO");
    }
    return;
}
void Yes(bool condition){

    if(condition){
        p("Yes");
    }else{
        p("No");
    }
    return;
}

/*
ll fact[800005],rfact[800005];

void c3_init(){
    fact[0] = rfact[0] = 1;
    for(ll i=1; i<=800000; i++){
        fact[i] = (fact[i-1]*i) % mod;
    }
	rfact[800000] = rui(fact[800000],mod - 2);
	for(ll i=800000; i>=1; i--){
	   rfact[i-1] = rfact[i] * i;
	   rfact[i-1] %= mod;
	}
	return;}
ll c3(ll n,ll r){
    return (((fact[n] * rfact[r]) % mod) * rfact[n-r]) % mod;}
*/

ll n,m,num,sum,ans,a,b,c,d,e,g,h,w,i,j,k,q;
ll x[300005],y[300005],z[100005];
ll dp[500005][15];
char s[500005];

int main(){
	cin >> s;
    n = strlen(s);
    dp[0][0] = 1;
    for(i=0;i<n;i++){
        for(j=0;j<13;j++){
            if(s[i] == '?'){
                for(k=0;k<=9;k++){
                    dp[i+1][(j * 10 + k) % 13] += dp[i][j];
                    dp[i+1][(j * 10 + k) % 13] %= mod;
                }
            }else{
                dp[i+1][(j * 10 + (s[i] - '0')) % 13] += dp[i][j];
                dp[i+1][(j * 10 + (s[i] - '0')) % 13] %= mod;
            }
        }
    }
    for(i=0;i<n;i++){
        //p(dp[i][0]);
    }
   // line;
    p(dp[n][5]);
    
	return 0;
}