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: Accepted)

import sys
 
s= sys.stdin.readline().strip()
#
MOD=10**9+7
mmap= []
for i in range(6):
    b = 10**i % 13
    mmap.append( [ [ (b*i+j)%13 for i in range(1,10) ] for j in range(13) ] )
#
dp= [ 0 ] * 13
dp[0] = 1
j= 0
for c in reversed(s):
    tmp = dp.copy()
    #
    if c=="0": pass
    elif c=="?":
        bset = mmap[j]
        for m,num in enumerate(tmp):
            if num==0: continue
            for idx in bset[m]: dp[idx]+=num
        #
        for i in range(13): dp[i]%=MOD
    else:
        b= mmap[j][0][int(c)-1]
        for m in range(13):
            idx= (m+b)%13
            dp[idx]= tmp[m]
    #
    if j==5: j=0
    else: j+=1
#
print(dp[5])