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 LuaJIT (2.0.4) (judge verdict: Accepted)

local mod = 1000000007
local mfl = math.floor

local s = io.read()
local n = #s
local t = {}
for i = 1, n do
  t[i] = {}
  for j = 0, 12 do
    t[i][j] = 0
  end
end
local sstr = s:sub(1, 1)
if sstr == "?" then
  for i = 0, 9 do
    t[1][i] = 1
  end
else
  t[1][tonumber(sstr)] = 1
end

local jumptbl = {0, 10, 7, 4, 1, 11, 8, 5, 2, 12, 9, 6, 3}

for i = 2, n do
  -- times 10
  local tmp = {}
  for j = 0, 12 do
    tmp[jumptbl[j + 1]] = t[i - 1][j]
  end
  for j = 0, 12 do
    t[i - 1][j] = tmp[j]
  end
  -- add
  sstr = s:sub(i, i)
  if sstr == "?" then
    for num = 0, 9 do
      for j = 0, 12 do
        t[i][(j + num) % 13] = (t[i][(j + num) % 13] + t[i - 1][j]) % 1000000007
      end
    end
  else
    local num = tonumber(sstr)
    for j = 0, 12 do
      t[i][(j + num) % 13] = t[i - 1][j]
    end
  end
end
print(t[n][5])