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)

//------------------------------------------------------------------------------MANAS UNIYAL---------------------------------------------------------
//																				NEVER GIVE UP
#include<bits/stdc++.h>
using namespace std;
#define fast ios_base::sync_with_stdio(false);	cin.tie(NULL);	cout.tie(NULL);
#define ll long long
#define pb push_back
#define fi first
#define se second
#define pii pair<ll,ll>
#define INF 0x3f3f3f3f
#define mod 100000007
#define testcases() ll t; cin>>t; while(t--)
#define debug1(x) cout<<#x<<" "<<x<<"\n";
#define debug2(x,y) cout<<#x<<" "<<x<<" "<<#y<<" "<<y<<"\n";
#define debug3(x,y,z) cout<<#x<<" "<<x<<" "<<#y<<" "<<y<<" "<<#z<<" "<<z<<"\n";
#define rep(i,start,end) for(ll i=start;i<end;i++)
 
//----------------------------------------------------------------------------------------------------------------------------------------------------

int main()
{
	fast;
	string str;
	cin>>str;
	int n=(int)str.size();
	ll dp[100005][13];
	memset(dp,0,sizeof(dp));
	dp[0][0]=1;
	bool flag = false;
	int fix;
	for(int idx=0;idx<=n;idx++)
	{
		if(str[idx]=='?')
			flag = true;
		else
		{
			flag = false;
			fix = str[idx]-'0';
		}
		for(int digit=0;digit<=9;digit++)
		{
			if(!flag && digit!=fix)
				continue;
			for(int rem=0;rem<=12;rem++)
			{
				dp[idx+1][(rem*10+digit)%13]+=dp[idx][rem];
			}
		}
        for(int rem=0;rem<=12;rem++)
            dp[idx+1][rem]%=1000000007;
	}
	cout<<dp[n][5];
	return 0;
}