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 Lua (5.3.2) (judge verdict: Accepted)

local read = setmetatable({}, {__index = function(t, k) local a = {} for i=1,#k do table.insert(a, '*'..string.sub(k, i, i)) end local r = io.read local u = table.unpack or unpack return function() return r(u(a)) end end})
read.N = function(N) local t={} for i=1,N do t[i]=read.n() end return t end
string.totable = function(s) local t={} local u=string.sub for i=1,#s do t[i] = u(s, i, i) end return t end
string.split = function(s) local t={} for w in string.gmatch(s, "[^%s]+") do table.insert(t, w) end return (table.unpack or unpack)(t) end
local function array(dimension, default_val) local n=dimension local m={}if default_val~=nil then m[1]={__index=function()return default_val end}end for i=2,n do m[i]={__index=function(p, k)local c=setmetatable({},m[i-1])rawset(p,k,c)return c end}end return setmetatable({},m[n])end
----
local MOD = math.floor(10^9)+7

local tmp = read.l():totable()
local S = {}
for i=1,#tmp do
    if tmp[i] == '?' then
        S[i] = '?'
    else
        S[i] = tonumber(tmp[i])
    end
end

local N = #S
local ti = array(1, 0)
local tio = array(1, 0)
tio[0] = 1
for i=1,N do
    if S[i] == '?' then
        local oldsum = tio[0] + tio[1] + tio[2] + tio[3] + tio[4] + tio[5] + tio[6] + tio[7] + tio[8] + tio[9] + tio[10] + tio[11] + tio[12]
        ti[0] = (oldsum - tio[4] - tio[8] - tio[12]) % MOD
        ti[1] = (oldsum - tio[3] - tio[8] - tio[12]) % MOD
        ti[2] = (oldsum - tio[3] - tio[7] - tio[12]) % MOD
        ti[3] = (oldsum - tio[3] - tio[7] - tio[11]) % MOD
        ti[4] = (oldsum - tio[2] - tio[7] - tio[11]) % MOD
        ti[5] = (oldsum - tio[2] - tio[6] - tio[11]) % MOD
        ti[6] = (oldsum - tio[2] - tio[6] - tio[10]) % MOD
        ti[7] = (oldsum - tio[1] - tio[6] - tio[10]) % MOD
        ti[8] = (oldsum - tio[1] - tio[5] - tio[10]) % MOD
        ti[9] = (oldsum - tio[1] - tio[5] - tio[9]) % MOD
        ti[10] = (oldsum - tio[0] - tio[5] - tio[9]) % MOD
        ti[11] = (oldsum - tio[0] - tio[4] - tio[9]) % MOD
        ti[12] = (oldsum - tio[0] - tio[4] - tio[8]) % MOD
    else
        local c = S[i]
        ti[(0 + c) % 13] = tio[0]
        ti[(10 + c) % 13] = tio[1]
        ti[(20 + c) % 13] = tio[2]
        ti[(30 + c) % 13] = tio[3]
        ti[(40 + c) % 13] = tio[4]
        ti[(50 + c) % 13] = tio[5]
        ti[(60 + c) % 13] = tio[6]
        ti[(70 + c) % 13] = tio[7]
        ti[(80 + c) % 13] = tio[8]
        ti[(90 + c) % 13] = tio[9]
        ti[(100 + c) % 13] = tio[10]
        ti[(110 + c) % 13] = tio[11]
        ti[(120 + c) % 13] = tio[12]
    end
    tio, ti = ti, tio
end
print(tio[5])