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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <string.h>
#define ll long long
#define MOD 1000000007
#define rep(i,l,r) for((i)=(l);(i)<(r);(i)++)
ll dp[100010][13];
char s[100010];
int main(){
	scanf("%s",s);
	int n=strlen(s),x,y,i;
	dp[0][0]=1;
	rep(i,0,n){
		if(s[i]=='?'){
			rep(x,0,13)rep(y,0,10)dp[i+1][(x*10+y)%13]+=dp[i][x]%MOD;
		}else{
			y=s[i]-'0';
			rep(x,0,13)dp[i+1][(x*10+y)%13]+=dp[i][x]%MOD;
		}
	}
	printf("%lld\n",dp[n][5]);
}