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)

#pragma GCC optimize("O3", "unroll-loops")
#pragma GCC target("avx2")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define int long long
#define double long double
#define endl "\n"
#define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define pb(x) push_back(x)
#define mp(a,b) make_pair(a,b)
#define ms(v,x) memset(v,x,sizeof(v))
#define pii pair<int,int>
#define ff first
#define ss second
#define frr(i,n) for(int i=0;i<n;i++)
#define td(v) v.begin(),v.end()
#define inf 1000000000 // 1e9
#define M   1000000007 // 1e9 + 7
using namespace std;
inline int mod(int n, int m){ int ret = n%m; if(ret < 0) ret += m; return ret; }
int gcd(int a, int b){return (b == 0 ? a : gcd(b, a%b));}
int lcm(int a,int b){return (a*b)/gcd(a,b);}
int exp(int a,int b,int m){
    if(b==0) return 1;
    if(b==1) return mod(a,m);
    int k = mod(exp(a,b/2,m),m);
    if(b&1){
        return mod(a*mod(k*k,m),m);
    }
    else return mod(k*k,m);
}
string s;
int v[] = {1,10,9,12,3,4};
int dp[100100][13];
int f(char c){
    return (c-'0');
}
int add(int a,int b){
    int ret = a + b;
    if(ret >= M) ret-= M;
    return ret;
}
int solve(int idx,int mdl){
    int &x = dp[idx][mdl];
    if(x!=-1){
        return x;
    }
    if(s[idx]!='?'){
        return x = solve(idx+1,(mdl + f(s[idx]) * v[idx%6]) % 13 );
    }
    else{
        x = 0;
        for(int i=0;i<=9;i++){
            x = add(x,solve(idx+1, (mdl + i * v[idx%6])%13 )) ;
        }
        return x;
    }
}
int32_t main(){
    fastio;
    cin >> s;
    reverse(td(s));
    ms(dp,-1);
    for(int i=0;i<13;i++) dp[s.size()][i] = 0;
    dp[s.size()][5] = 1;
    cout << solve(0,0) << endl;
}