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 PyPy2 (5.6.0) (judge verdict: Time Limit Exceeded)

# -*- coding: utf-8 -*-
import sys
S=sys.stdin.readline().strip()
N=len(S)
mod=10**9+7

dp=[ [ 0 for j in range(13) ] for i in range(N) ]

for i,x in enumerate(S[::-1]):  #i桁目
    if i==0:
        if x!="?":
            x=int(x)
            dp[i][(x*10**i)%13]=1
        else:
            for x in range(10):
                dp[i][(x*10**i)%13]=1
    else:
        if x!="?":
            x=int(x)
            for j in range(13):
                dp[i][(x*pow(10,i,13)+j)%13]+=dp[i-1][j]
        else:
            for j in range(13):
                for x in range(10):
                    dp[i][(x*pow(10,i,13)+j)%13]+=dp[i-1][j]
print dp[N-1][5]%mod