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)

import sys
sys.setrecursionlimit(10**7)
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x) - 1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def II(): return int(sys.stdin.readline())
def SI(): return sys.stdin.readline().strip()
INF = 10 ** 18
MOD = 10 ** 9 + 7


from functools import lru_cache


def main(): 
    S = SI()

    # 桁DP
    dp_table = [[0 for _ in range(13)] for _ in range(len(S))]

    # 最初の桁を見る。
    if S[0] == '?':
        for i in range(10):
            dp_table[0][i] = 1
    else:
        dp_table[0][int(S[0])] = 1

    # 以降の桁を見ていく。
    for digit in range(1, len(S)):
        if S[digit] == '?':
            for prev_res, comb in enumerate(dp_table[digit-1]):
                for x in range(10):
                    res = (prev_res*10+x)%13
                    dp_table[digit][res] = (dp_table[digit][res] + comb)%MOD

        else:
            for prev_res, comb in enumerate(dp_table[digit-1]):
                res = (prev_res*10+int(S[digit]))%13
                dp_table[digit][res] = (dp_table[digit][res] + comb)%MOD

    print(dp_table[len(S)-1][5])





main()