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 <cstdio>
#include <utility>
using namespace std;

using i64 = long long;

#define REP(i, stop) for (int i = 0, i##_len = stop; i < i##_len; ++i)

i64 D[13];
i64 E[13];
const i64 M = 1000000007;
signed main() {
	D[0] = 1;
	while(true) {
		char c = getchar_unlocked();
		if (c == '\n') {
			break;
		} else if (c == '?') {
			REP(r, 13) {
				i64 s = 0;
				REP(j, 10) {
					s += D[(j - r + 13) * 9 % 13];
				}
				E[r] = s % M;
			}
		} else {
			i64 d = c - '0';
			REP(r, 13) {
				E[r] = D[(d - r + 13) * 9 % 13];
			}
		}
		swap(D, E);
	}
	printf("%d", D[5]);
}