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: Runtime Error)

import sys
input=sys.stdin.readline

S=input()
n=len(S)
R=[0]*13 #剰余テーブル
cnt=[0]*13
Pow=[[] for i in range(6)] #10の累乗の剰余テーブル
mod=10**9+7

for i in range(6):
    c=10**i
    for j in range(10):
        Pow[i].append(c*j%13)
print(Pow)
ans=0
flag=0
for i in range(n):
    if S[n-i-1]=="?":
        P=Pow[i%6] #当該の剰余テーブル
        if flag==0:
            for p in P:
                R[p]=1
                flag=1
        else:
            for j in range(10):
                for k in range(13):
                    cnt[(k+P[j])%13]+=R[k]%mod
            R=cnt
            cnt=[0]*13
    else:
        x=int(S[n-i-1])
        ans+=Pow[i%6][x]
        print(x,ans)
    print(R,i)
    print(sum(R))
ans%=13
print(R[(18-ans)%13]%mod)