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: Runtime Error)

'use strict';

function _slicedToArray(arr, i) { return _arrayWithHoles(arr) || _iterableToArrayLimit(arr, i) || _unsupportedIterableToArray(arr, i) || _nonIterableRest(); }

function _nonIterableRest() { throw new TypeError("Invalid attempt to destructure non-iterable instance.\nIn order to be iterable, non-array objects must have a [Symbol.iterator]() method."); }

function _unsupportedIterableToArray(o, minLen) { if (!o) return; if (typeof o === "string") return _arrayLikeToArray(o, minLen); var n = Object.prototype.toString.call(o).slice(8, -1); if (n === "Object" && o.constructor) n = o.constructor.name; if (n === "Map" || n === "Set") return Array.from(o); if (n === "Arguments" || /^(?:Ui|I)nt(?:8|16|32)(?:Clamped)?Array$/.test(n)) return _arrayLikeToArray(o, minLen); }

function _arrayLikeToArray(arr, len) { if (len == null || len > arr.length) len = arr.length; for (var i = 0, arr2 = new Array(len); i < len; i++) { arr2[i] = arr[i]; } return arr2; }

function _iterableToArrayLimit(arr, i) { if (typeof Symbol === "undefined" || !(Symbol.iterator in Object(arr))) return; var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"] != null) _i["return"](); } finally { if (_d) throw _e; } } return _arr; }

function _arrayWithHoles(arr) { if (Array.isArray(arr)) return arr; }

function main(lines) {
  var _lines = _slicedToArray(lines, 1),
      S = _lines[0];

  var table = new Array(Math.pow(10, 5) + 1).fill().map(function () {
    return new Array(13).fill();
  });
  table[0].fill(0);
  table[0][0] = 1;

  var _loop = function _loop(digits) {
    var _loop2 = function _loop2(reminder) {
      var c = S[digits - 1];

      if (c === '?') {
        table[digits][reminder] = new Array(10).fill().reduce(function (acc, _, n) {
          var val = new Array(13).fill().map(function (_, i) {
            return i;
          }).filter(function (rem) {
            return (rem * 10 + n) % 13 === reminder;
          }).reduce(function (acc, rem) {
            return table[digits - 1][rem] + acc;
          }, 0);
          return val + acc;
        }, 0) % (Math.pow(10, 9) + 7);
        return "continue";
      }

      var n = Number(c);
      table[digits][reminder] = new Array(13).fill().map(function (_, i) {
        return i;
      }).filter(function (rem) {
        return (rem * 10 + n) % 13 === reminder;
      }).reduce(function (acc, rem) {
        return dp[digits - 1][rem] + acc;
      }, 0) % (Math.pow(10, 9) + 7);
    };

    for (var reminder = 0; reminder < 13; reminder++) {
      var _ret = _loop2(reminder);

      if (_ret === "continue") continue;
    }
  };

  for (var digits = 1; digits <= S.length; digits++) {
    _loop(digits);
  }

  function dp(digits, reminder) {
    if (digits === 0 && reminder === 0) return 1;
    if (digits === 0) return 0;
    var val = table[digits][reminder];
    if (val !== undefined) return val;
    var c = S[digits - 1];

    if (c === '?') {
      return table[digits][reminder] = new Array(10).fill().reduce(function (acc, _, n) {
        var val = new Array(13).fill().map(function (_, i) {
          return i;
        }).filter(function (rem) {
          return (rem * 10 + n) % 13 === reminder;
        }).reduce(function (acc, rem) {
          return dp(digits - 1, rem) + acc;
        }, 0);
        return val + acc;
      }, 0) % (Math.pow(10, 9) + 7);
    }

    var n = Number(c);
    return table[digits][reminder] = new Array(13).fill().map(function (_, i) {
      return i;
    }).filter(function (rem) {
      return (rem * 10 + n) % 13 === reminder;
    }).reduce(function (acc, rem) {
      return dp(digits - 1, rem) + acc;
    }, 0) % (Math.pow(10, 9) + 7);
  } // console.log(dp(S.length, 5));


  console.log(table[S.length][5]);
}

function runWithStdin() {
  var input = "";
  process.stdin.resume();
  process.stdin.setEncoding("utf8");
  process.stdin.on("data", function (v) {
    input += v;
  });
  process.stdin.on("end", function () {
    main(input.split("\n"));
  });
}

runWithStdin();