Problem:
Score : 400 points

Problem Statement

Along a road running in an east-west direction, there are A shrines and B temples.
The i-th shrine from the west is located at a distance of s_i meters from the west end of the road, and the i-th temple from the west is located at a distance of t_i meters from the west end of the road.

Answer the following Q queries:

Query i (1 \leq i \leq Q): If we start from a point at a distance of x_i meters from the west end of the road and freely travel along the road, what is the minimum distance that needs to be traveled in order to visit one shrine and one temple? (It is allowed to pass by more shrines and temples than required.)

Constraints

1 \leq A, B \leq 10^5

1 \leq Q \leq 10^5

1 \leq s_1 < s_2 < ... < s_A \leq 10^{10}

1 \leq t_1 < t_2 < ... < t_B \leq 10^{10}

1 \leq x_i \leq 10^{10}

s_1, ..., s_A, t_1, ..., t_B, x_1, ..., x_Q are all different.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

A B Q
s_1
:
s_A
t_1
:
t_B
x_1
:
x_Q

Output

Print Q lines. The i-th line should contain the answer to the i-th query.

Sample Input 1

2 3 4
100
600
400
900
1000
150
2000
899
799

Sample Output 1

350
1400
301
399

There are two shrines and three temples. The shrines are located at distances of 100, 600 meters from the west end of the road, and the temples are located at distances of 400, 900, 1000 meters from the west end of the road.

Query 1: If we start from a point at a distance of 150 meters from the west end of the road, the optimal move is first to walk 50 meters west to visit a shrine, then to walk 300 meters east to visit a temple.

Query 2: If we start from a point at a distance of 2000 meters from the west end of the road, the optimal move is first to walk 1000 meters west to visit a temple, then to walk 400 meters west to visit a shrine. We will pass by another temple on the way, but it is fine.

Query 3: If we start from a point at a distance of 899 meters from the west end of the road, the optimal move is first to walk 1 meter east to visit a temple, then to walk 300 meters west to visit a shrine.

Query 4: If we start from a point at a distance of 799 meters from the west end of the road, the optimal move is first to walk 199 meters west to visit a shrine, then to walk 200 meters west to visit a temple.

Sample Input 2

1 1 3
1
10000000000
2
9999999999
5000000000

Sample Output 2

10000000000
10000000000
14999999998

The road is quite long, and we may need to travel a distance that does not fit into a 32-bit integer.

Solution in JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)

"use strict";

function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }

function _defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } }

function _createClass(Constructor, protoProps, staticProps) { if (protoProps) _defineProperties(Constructor.prototype, protoProps); if (staticProps) _defineProperties(Constructor, staticProps); return Constructor; }

function _toArray(arr) { return _arrayWithHoles(arr) || _iterableToArray(arr) || _nonIterableRest(); }

function _toConsumableArray(arr) { return _arrayWithoutHoles(arr) || _iterableToArray(arr) || _nonIterableSpread(); }

function _nonIterableSpread() { throw new TypeError("Invalid attempt to spread non-iterable instance"); }

function _iterableToArray(iter) { if (Symbol.iterator in Object(iter) || Object.prototype.toString.call(iter) === "[object Arguments]") return Array.from(iter); }

function _arrayWithoutHoles(arr) { if (Array.isArray(arr)) { for (var i = 0, arr2 = new Array(arr.length); i < arr.length; i++) { arr2[i] = arr[i]; } return arr2; } }

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

function _nonIterableRest() { throw new TypeError("Invalid attempt to destructure non-iterable instance"); }

function _iterableToArrayLimit(arr, i) { 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() {
  // ----------
  (function (input) {
    var lines = input.split("\n");

    var _splitNum = splitNum(lines[0]),
        _splitNum2 = _slicedToArray(_splitNum, 3),
        A = _splitNum2[0],
        B = _splitNum2[1],
        Q = _splitNum2[2];

    var s = splitNum(lines.slice(1).slice(0, A));
    var t = splitNum(lines.slice(1 + A).slice(0, B));
    var xs = splitNum(lines.slice(1 + A + B).slice(0, Q));
    var _iteratorNormalCompletion = true;
    var _didIteratorError = false;
    var _iteratorError = undefined;

    try {
      for (var _iterator = xs[Symbol.iterator](), _step; !(_iteratorNormalCompletion = (_step = _iterator.next()).done); _iteratorNormalCompletion = true) {
        var x = _step.value;
        // search for nearby S.
        var sNearby = binarySearch(s, x);
        var min = Infinity;
        var _iteratorNormalCompletion2 = true;
        var _didIteratorError2 = false;
        var _iteratorError2 = undefined;

        try {
          for (var _iterator2 = [sNearby.low.value, sNearby.high.value].filter(function (x) {
            return !isNaN(x);
          })[Symbol.iterator](), _step2; !(_iteratorNormalCompletion2 = (_step2 = _iterator2.next()).done); _iteratorNormalCompletion2 = true) {
            var y = _step2.value;

            var _tNearby = binarySearch(t, y);

            var res = Math.abs(x - y) + minIgnoreNaN(Math.abs(_tNearby.low.value - y), Math.abs(_tNearby.high.value - y));

            if (min > res) {
              min = res;
            }
          }
        } catch (err) {
          _didIteratorError2 = true;
          _iteratorError2 = err;
        } finally {
          try {
            if (!_iteratorNormalCompletion2 && _iterator2.return != null) {
              _iterator2.return();
            }
          } finally {
            if (_didIteratorError2) {
              throw _iteratorError2;
            }
          }
        }

        var tNearby = binarySearch(t, x);
        var _iteratorNormalCompletion3 = true;
        var _didIteratorError3 = false;
        var _iteratorError3 = undefined;

        try {
          for (var _iterator3 = [tNearby.low.value, tNearby.high.value].filter(function (x) {
            return !isNaN(x);
          })[Symbol.iterator](), _step3; !(_iteratorNormalCompletion3 = (_step3 = _iterator3.next()).done); _iteratorNormalCompletion3 = true) {
            var _y = _step3.value;

            var _sNearby = binarySearch(s, _y);

            var _res = Math.abs(x - _y) + minIgnoreNaN(Math.abs(_sNearby.low.value - _y), Math.abs(_sNearby.high.value - _y));

            if (min > _res) {
              min = _res;
            }
          }
        } catch (err) {
          _didIteratorError3 = true;
          _iteratorError3 = err;
        } finally {
          try {
            if (!_iteratorNormalCompletion3 && _iterator3.return != null) {
              _iterator3.return();
            }
          } finally {
            if (_didIteratorError3) {
              throw _iteratorError3;
            }
          }
        }

        console.log(min);
      }
    } catch (err) {
      _didIteratorError = true;
      _iteratorError = err;
    } finally {
      try {
        if (!_iteratorNormalCompletion && _iterator.return != null) {
          _iterator.return();
        }
      } finally {
        if (_didIteratorError) {
          throw _iteratorError;
        }
      }
    }

    function binarySearch(arr, target) {
      var start = 0,
          end = arr.length;

      while (start + 1 < end) {
        var mid = Math.ceil((end + start) / 2);
        var val = arr[mid];

        if (val <= target) {
          start = mid;
        } else {
          end = mid;
        }
      }

      if (start === end) {
        return {
          exact: true,
          low: {
            index: start,
            value: arr[start]
          },
          high: {
            index: start,
            value: arr[start]
          }
        };
      } else {
        return {
          exact: false,
          low: {
            index: start,
            value: arr[start]
          },
          high: {
            index: start + 1,
            value: arr[start + 1]
          }
        };
      }
    }

    function minIgnoreNaN() {
      for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {
        args[_key] = arguments[_key];
      }

      return Math.min.apply(Math, _toConsumableArray(args.filter(function (x) {
        return !isNaN(x);
      })));
    }
  })(require("fs").readFileSync("/dev/stdin", "utf8"));

  function splitNum(line) {
    return (Array.isArray(line) ? line : line.split(/\s+/)).map(function (n) {
      return parseInt(n);
    });
  }
  /**
   * Iterates over integers in [start, end).
   */


  /**
   * implementation of arbitrary-precision unsigned integer.
   */
  var Longer =
  /*#__PURE__*/
  function () {
    function Longer(value) {
      _classCallCheck(this, Longer);

      // enough for 64bit
      this.data = [0, 0, 0];
      var idx = 0;

      while (value !== 0) {
        this.data[idx] = value % Longer.border;
        value = Math.floor(value / Longer.border);
        idx++;
      }
    }

    _createClass(Longer, [{
      key: "add",
      value: function add(right) {
        var result = new Longer(0);
        var max = Math.max(this.data.length, right.data.length);
        var carry = 0;
        var idx = 0;

        for (; idx < max; idx++) {
          var sum = (this.data[idx] || 0) + (right.data[idx] || 0) + carry;
          result.data[idx] = sum % Longer.border;
          carry = Math.floor(sum / Longer.border);
        }

        if (carry > 0) {
          result.data[idx] = carry;
        }

        return result;
      }
    }, {
      key: "mul",
      value: function mul(right) {
        var result = new Longer(0);

        for (var lidx = 0; lidx < this.data.length; lidx++) {
          for (var ridx = 0; ridx < right.data.length; ridx++) {
            var me = this.data[lidx] * right.data[ridx];
            var tidx = lidx + ridx;
            var value = me;

            while (value > 0) {
              var sum = (result.data[tidx] || 0) + value;
              result.data[tidx] = sum % Longer.border;
              value = Math.floor(sum / Longer.border);
              tidx++;
            }
          }
        }

        return result;
      }
    }, {
      key: "toString",
      value: function toString() {
        var d = this.data.concat().reverse(); // let fsti = d.findIndex(v => v !== 0);

        var fsti = function (arr, pred) {
          for (var i = 0; i < arr.length; i++) {
            if (pred(arr[i], i)) {
              return i;
            }
          }

          return null;
        } // not full polyfill!
        (d, function (v) {
          return v !== 0;
        });

        if (fsti == null) {
          return "0";
        }

        return d.slice(fsti).map(function (v, i) {
          if (i === 0) {
            return String(v);
          } else {
            // return String(v).padStart(Longer.digits, "0");
            return padStart(String(v), Longer.digits, "0");
          }
        }).join("");

        function padStart(str, num, pad) {
          var n = num - str.length;
          var result = "";

          for (var i = 0; i < n; i++) {
            result += pad;
          }

          return result + str;
        }
      }
    }]);

    return Longer;
  }();
  /** digits per element. */


  Longer.digits = 7;
  Longer.border = Math.pow(10, Longer.digits);
  /**
   * Runs a recursive function expressed as a generator function.
   */
  // ----------
}

_main();