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 Python (3.4.3) (judge verdict: Runtime Error)

from operator import itemgetter
import sys
input = sys.stdin.readline
 
S = input()
 
table = [[0] * 13 for i in range(len(S))]
 
if S[len(S)-1] == '?':
    for i in range(10):
        table[0][i] = 1
else:
    table[0][int(S[len(S)-1])] = 1
 
for i in range(len(S)-1):    
    if S[len(S)-i-2] =='?':
        for j in range(10):
            mod = (10**(i+1)) * j % 13
            for k in range(13):
                table[i+1][(k+mod) % 13] += table[i][k] #% (10**9 + 7)
    else:
        num = int(S[len(S)-i-2])
        mod = (10**(i+1)) * num % 13
        for k in range(13):
            table[i+1][(k+mod) % 13] += table[i][k] #% (10**9 + 7)
            
print(table[len(S)-1][5]%(10**9+7))