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 <bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define REP(i,n) for (int i = 1; i < (int)(n); i++)
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define vout(x) rep(i,x.size()) cout << x[i] << " "
template<class T> bool chmin(T &a, T b) {if(a>b) {a=b;return 1;}return 0;}
template<class T> bool chmax(T &a, T b) {if(a<b) {a=b;return 1;}return 0;}
using namespace std;
using vint = vector<int>;
using vvint = vector<vector<int>>;
using ll = long long;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using P = pair<int,int>;
const int inf = 1e9;
const ll inf_l = 1e18;
const int MAX = 1e5;
const int mod = 1e9+7;

ll dp[13];

int main() {
    string s; cin >> s;
    int n = s.size();
    vint mo(n);
    mo[n-1] = 1;
    for (int i = n-2; i >= 0; i--) {
        mo[i] = (mo[i+1]*10)%13;
    }
    dp[0] = 1;
    for (int i = n-1; i >= 0; i--) {
        ll next_dp[13];
        rep(i,13) next_dp[i] = 0;
        if (s[i] != '?') {
            int x = (s[i] - '0')*mo[i]%13;
            rep(j,13) {
                next_dp[(j+x)%13] += dp[j];
            }
        }
        else {
            rep(j,13) {
                rep(k,10) {
                    int x = k*mo[i]%13;
                    next_dp[(j+x)%13] += dp[j];
                }
            }
        }
        rep(i,13) next_dp[i] %= mod;
        swap(dp,next_dp);
    }
    cout << dp[5] << endl;
}