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<(n); i++)
#define chmax(x, y) x = max(x, y)
#define chmin(x, y) x = min(x, y)
using namespace std;
typedef long long ll;

const int MOD = 1000000007;

int dp[100010][13];

int main() {
    string S;
    cin >> S;

    dp[0][0] = 1;
    for (int i = 0; i < S.size(); i++) {
        if (S[i] == '?') {
            rep(k, 10) { // 0 ～ 9 まで試す
                rep(j, 13) {
                    int nextRem = (j * 10 + k) % 13;
                    dp[i + 1][nextRem] += dp[i][j];
                    dp[i + 1][nextRem] %= MOD;
                }
            }
        } else {
            int k = S[i] - '0';
            rep(j, 13) {
                int nextRem = (j * 10 + k) % 13;
                dp[i + 1][nextRem] += dp[i][j];
                dp[i + 1][nextRem] %= MOD;
            }
        }
    }

    cout << dp[S.size()][5] << endl;
}