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)

// {{{ by unolight
#include <bits/stdc++.h>
#include <unistd.h>
#pragma GCC diagnostic ignored "-Wunused-result"
#define SZ(x) ((int)(x).size())
#define ALL(x) begin(x),end(x)
#define RALL(x) rbegin(x),rend(x)
#define REP(i,n) for ( int i=0; i<int(n); i++ )
#define REP1(i,a,b) for ( int i=(a); i<=int(b); i++ )
#define MP make_pair
#define PB push_back
using namespace std;
typedef int64_t LL;
typedef pair<int,int> PII;
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;

template<class T> void _R( T &x ) { cin>>x; }
void _R( int &x ) { scanf("%d",&x); }
void _R( int64_t &x ) { scanf("%" PRId64,&x); }
void _R( double &x ) { scanf("%lf",&x); }
void _R( char &x ) { scanf(" %c",&x); }
void _R( char *x ) { scanf("%s",x); }
void R() {}
template<class T, class... U> void R( T& head, U&... tail ) { _R(head); R(tail...); }

template<class T> void _W( const T &x ) { cout<<x; }
void _W( const int &x ) { printf("%d",x); }
void _W( const int64_t &x ) { printf("%" PRId64,x); }
void _W( const double &x ) { printf("%.16f\n",x); }
void _W( const char &x ) { putchar(x); }
void _W( const char *x ) { printf("%s",x); }
template<class T> void _W( const vector<T> &x ) { for (auto i = x.begin(); i != x.end(); _W(*i++)) if (i != x.cbegin()) putchar(' '); }
void W() {}
template<class T, class... U> void W( const T& head, const U&... tail ) { _W(head); putchar(sizeof...(tail)?' ':'\n'); W(tail...); }

template<class T> inline bool chmax( T &a, const T &b ) { return b>a ? a=b,true : false; }
template<class T> inline bool chmin( T &a, const T &b ) { return b<a ? a=b,true : false; }
template<class T, class F=less<T>> void sort_uniq( vector<T> &v, F f=F() ) {
    sort(begin(v),end(v),f);
    v.resize(unique(begin(v),end(v))-begin(v));
}

template<class T> using MaxHeap = priority_queue<T>;
template<class T> using MinHeap = priority_queue<T, vector<T>, greater<T>>;

#ifdef UNO
template<class T> void _dump(const char *s, T &&head) { cerr << s << "=" << head << endl; }
template<class T, class... Args> void _dump(const char *s, T &&head, Args &&... tail) {
    for (int c = 0; *s != ',' || c != 0; cerr << *s++) {
        if (*s == '(' || *s == '[' || *s == '{') c++;
        if (*s == ')' || *s == ']' || *s == '}') c--;
    }
    cerr << "=" << head << ", ";
    _dump(s + 1, tail...);
}
#define dump(...) do { fprintf(stderr, "%s:%d - ", __PRETTY_FUNCTION__, __LINE__); _dump(#__VA_ARGS__, __VA_ARGS__); } while (0)

template<class Iter> ostream &_out(ostream &s, Iter b, Iter e) {
    s << "[";
    for (auto it = b; it != e; it++) s << (it == b ? "" : " ") << *it;
    return s << "]";
}

template<class A, class B> ostream &operator<<(ostream &s, const pair<A, B> &p) { return s << "(" << p.first << "," << p.second << ")"; }
template<class T> ostream &operator<<(ostream &s, const vector<T> &c) { return _out(s, ALL(c)); }
template<class T, size_t N> ostream &operator<<(ostream &s, const array<T, N> &c) { return _out(s, ALL(c)); }
template<class T> ostream &operator<<(ostream &s, const set<T> &c) { return _out(s, ALL(c)); }
template<class A, class B> ostream &operator<<(ostream &s, const map<A, B> &c) { return _out(s, ALL(c)); }
#else
#define dump(...)
#endif
// }}}

const int MAX_N=1e5+10, mod=1e9+7;
string s;
LL n, dp[MAX_N][13];

void add(LL &a, LL b) {
    (a+=b)%=mod;
}

int main() {
    R(s);
    n = s.length();
    dp[0][0]=1;
    REP(i, n) {
        int c = s[i]=='?'? -1:s[i]-'0';
        REP(j, 13) {
            if(c<0) {
                REP(k, 10) add(dp[i+1][(j*10+k)%13], dp[i][j]);
            } else {
                add(dp[i+1][(j*10+c)%13], dp[i][j]);
            }            
        }
    }

    W(dp[n][5]);
    return 0;
}