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)

#!/usr/bin/env python
# coding: utf-8

""" """

import argparse


def parse_arguments():
    parser = argparse.ArgumentParser(description=' ')
    parser.add_argument('-i', '--input_file', required=True)
    parser.add_argument('-o', '--output_file', required=True)
    args = parser.parse_args()
    return args

MOD = 10**9+7
def main():
    s = input()
    dp = [[0 for _ in range(13)] for _ in range(len(s)+1)]
    dp[0][0] = 1
    lm = dict()
    for d in range(10):
        for m in range(13):
            lm[(m,d)] = (10*m+d)%13
    for i in range(len(s)):
        c = s[i]
        if c != '?':
            d = int(c)
            for m in range(13):
                dp[i+1][lm[(m,d)]] += dp[i][m]
        else:
            for d in range(10):
                for m in range(13):
                    dp[i+1][lm[(m,d)]] += dp[i][m]
        if i & 1:
            for m in range(13):
                dp[i+1][m] %= MOD
    print(dp[len(s)][5] % MOD)


if __name__ == '__main__':
    # args = parse_arguments()
    main()