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: Time Limit Exceeded)

S = list(input())

DIVIDER = 13

mod_digit = [i % DIVIDER for i in range(10)]
mod_level = []
tmp = 1
for _ in range(len(S)):
    mod_level.append(tmp % DIVIDER)
    tmp *= 10
mod_level = mod_level[::-1]

memo = [[0] * DIVIDER for _ in range(len(S) + 1)]
# def dp(pos, mod_tmp):
for idx in range(len(S) + 1):
    # if pos < 0:
    #     if mod_tmp == 5:
    #         return 1
    #     else:
    #         return 0
    # elif memo[pos][mod_tmp] != None: return memo[pos][mod_tmp]
    if idx == 0:
        for mod_tmp in range(DIVIDER):
            if mod_tmp == 5:
                memo[0][mod_tmp] = 1
            else:
                memo[0][mod_tmp] = 0
    else:
        pos = idx - 1
        for mod_tmp in range(DIVIDER):
            ret = 0
            if S[pos] == '?':
                for d in range(10):
                    mod_nxt = (mod_tmp + mod_digit[d] * mod_level[pos]) % DIVIDER
                    ret += memo[idx - 1][mod_nxt]
            else:
                d = int(S[pos])
                mod_nxt = (mod_tmp + mod_digit[d] * mod_level[pos]) % DIVIDER
                ret += memo[idx - 1][mod_nxt]
            #
            memo[idx][mod_tmp] = ret % 1000000007

print(memo[len(S)][0])