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 JavaScript (node.js v5.12) (judge verdict: Accepted)

'use strict'
function main(inp) {
  inp = inp.trim()

  const MOD = 1000000007
  let dp = [new Array(13).fill(0)]
  dp[0][0] = 1
  
  for (let i = 0; i < inp.length; i++) {
    dp[i + 1] = new Array(13).fill(0)
    const c = inp[i] === '?' ? -1 : inp[i] - 0
    for (let j = 0; j < 10; j++) {
      if (c !== -1 && c !== j) continue
      for (let k = 0; k < 13; k++) {
        dp[i+1][(k * 10 + j) % 13] += dp[i][k]
      }
    }
    for (let j = 0; j < 13; j++) {
      dp[i+1][j] %= MOD
    }
  }
  console.log(dp[inp.length][5])
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));