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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

# encoding:utf-8
import copy
import random
import bisect #bisect_left　これで二部探索の大小検索が行える
import fractions #最小公倍数などはこっち
import math
import sys
import bisect

mod = 10**9+7
sys.setrecursionlimit(mod) # 再帰回数上限はでdefault1000

def LI(): return list(map(int, sys.stdin.readline().split()))

S = list(str(input()))
S.reverse()
extra = 0
each_extras = [[] for i in range(S.count("?"))]
cnt = 0
mul = 1
for i in range(len(S)):
    if S[i] != "?":
        extra += int(S[i]) * 10 ** i
        extra %= 13
    else:
        each_extras[cnt] = []
        for x in range(10):
            each_extras[cnt].append(x * mul % 13)
            # each_extras[cnt][x * 10 ** i % 13] = 1
        cnt += 1

    mul = mul * 10 % 13

# print(each_extras)

# print(extra)
dp = [[0 for i in range(13)] for j in range(cnt+1)]
dp[0][extra % 13] = 1
for i in range(cnt):
    for extras in each_extras[i]:
        for j in range(13):
            dp[i+1][(extras + j)%13] += dp[i][j]
            dp[i+1][(extras + j)%13] %= mod
    for j in range(13):
        dp[i+1][j] = dp[i+1][j] % mod


# print(dp)
print(dp[-1][5] % mod)

"""
S = list(str(input()))

dp = [[0 for i in range(13)]for j in range(len(S)+1)]
dp[0][0] = 1
S.reverse()
mul = 1
for i in range(len(S)):
    if S[i] == "?":
        for j in range(10):
            for k in range(13):
                dp[i+1][(mul*j+k)%13] += dp[i][k]
                dp[i+1][(mul*j+k)%13] %= mod
    else:
        for k in range(13):
            dp[i+1][(int(S[i])*mul+k)%13] += dp[i][k]
            dp[i+1][(int(S[i])*mul+k)%13] %= mod
    mul *= 10
    mul %= 13

# print(dp)
print(dp[-1][5])
"""