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: Runtime Error)

#include <bits/stdc++.h>
typedef long long ll;
using namespace std;
ll MOD = 1e9+7;

#define vec     vector<int>
#define vecll   vector<ll>
#define vec2    vector<vector<int>>
#define vec2ll  vector<vector<ll>>
#define vpair   vector<pair<int, int>>
#define vpairll vector<pair<ll, ll>>

#define rep(i,n)         for(int i=(int)0; i<(int)n; i++)
#define REP(i,m,n)       for(int i=(int)m; i<(int)n; i++)
#define arr(var, n)      vec var(n); rep(i,n){cin >> var[i];}
#define arrll(var, n)    vecll var(n); rep(i,n){cin >> var[i];}
#define all(var)         (var).begin(), (var).end()
#define sortall(var)     sort(all(var))
#define prt(var)         cout << var << "\n"
#define prtd(n, var)     cout << fixed << setprecision(n) << var << "\n"
#define prt2(v1, v2)     cout << v1 << " " << v2 << "\n"
#define prt3(v1, v2, v3) cout << v1 << " " << v2 << " " << v3 << "\n"
#define prtall(var)      rep(i,var.size()){cout << var[i] << " ";} cout << "\n"

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

int main(void) {
  int n, q;
  cin >> n >> q;
  string s;
  cin >> s;

  vec l(q), r(q);
  rep(i,q){
    cin >> l[i] >> r[i];
    l[i]; r[i];
  }

  vec num_ac(n+1);
  rep(i,n+1){
    num_ac[i]=0;
  }
  REP(i,1,n){
    if(s[i-1]=='A' && s[i]=='C'){
      num_ac[i+1]=num_ac[i]+1;
    } else {
      num_ac[i+1]=num_ac[i];
    }
  }
  //prtall(num_ac);

  rep(i,q){
    prt(num_ac[r[i]]-num_ac[l[i]]);
  }

}