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 <iostream>
#include <iomanip>
#include <cstring>
#include <algorithm> 
#include <math.h>
#include <queue>
#include <functional>
#include <map>
#include <vector>
#include <string>
#include <set> 
using namespace std;

typedef long long ll;
typedef pair<ll, int> P;
typedef pair<pair<int, int>, int> PP;

const ll INF = 1e15;
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };


const ll MAX = 510000;
const ll MOD =1000000007;

int sz=1;
ll dp[100010][20];

int main(void) {
	string S; cin >> S;
	int n = S.size();
	dp[0][0]=1;
	
	for (int i = 0; i < n; i++) {
		if (S[i] == '?') {
			for (int j = 0; j < 10; j++) {
				for (int k = 0; k < 13; k++) {
				    int m = (10*k+j)%13;
					dp[i + 1][m] += dp[i][k];
					dp[i + 1][m] %= MOD;
				}
			}
		}
		else {
			int c = S[i] - '0';
			for (int k = 0; k < 13; k++) {
				int m = (10*k+c)%13;
				dp[i + 1][m] += dp[i][k];
				dp[i + 1][m] %= MOD;
			}
		}
	}

	cout << dp[n][5] << endl;
	
}