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)

def INT_(n): return int(n)-1
def MI(): return map(int, input().split())
def MF(): return map(float, input().split())
def MI_(): return map(INT_, input().split())
def LI(): return list(MI())
def LI_(): return [int(x) - 1 for x in input().split()]
def LF(): return list(MF())
def LIN(n: int): return [I() for _ in range(n)]
def LLIN(n: int): return [LI() for _ in range(n)]
def LLIN_(n: int): return [LI_() for _ in range(n)]
def LLI(): return [list(map(int, l.split())) for l in input()]
def I(): return int(input())
def F(): return float(input())
def ST(): return input().replace('\n', '')
MOD = 10**9 + 7

import numpy as np

pow_mods = [1, 10, 9, 12, 3, 4]


def main():
    S = input()
    length = len(S)
    dp = np.zeros((length, 13), dtype=np.int64)
    # dp = [[0] * 13 for _ in range(length)]
    for idx, s in enumerate(S[::-1]):
        # power = length - idx - 1
        power = idx
        if s == '?':
            table = get_table(power)
            if idx == 0:
                for mod in table:
                    dp[idx, mod] += 1
                continue
            for mod in table:
                for j in range(13):
                    dp[idx, (j + mod) % 13] += dp[idx - 1, j] % MOD
        else:
            mod = (int(s) * pow_mods[power % 6]) % 13
            if idx == 0:
                dp[idx, mod] = 1
                continue
            for j in range(13):
                dp[idx, (j + mod) % 13] += dp[idx - 1, j] % MOD

    print(dp[-1][5] % MOD)


def get_table(n):
    return [(i * pow_mods[n % 6]) % 13 for i in range(10)]


if __name__ == '__main__':
    main()