Problem:
Score : 300 points

Problem Statement

Given are positive integers N, M, Q, and Q quadruples of integers ( a_i , b_i , c_i , d_i ).

Consider a sequence A satisfying the following conditions:

A is a sequence of N positive integers.

1 \leq A_1 \leq A_2 \le \cdots \leq A_N \leq M.

Let us define a score of this sequence as follows:

The score is the sum of d_i over all indices i such that A_{b_i} - A_{a_i} = c_i. (If there is no such i, the score is 0.)

Find the maximum possible score of A.

Constraints

All values in input are integers.

2 ≤ N ≤ 10

1 \leq M \leq 10

1 \leq Q \leq 50

1 \leq a_i < b_i \leq N ( i = 1, 2, ..., Q )

0 \leq c_i \leq M - 1 ( i = 1, 2, ..., Q )

(a_i, b_i, c_i) \neq (a_j, b_j, c_j) (where i \neq j)

1 \leq d_i \leq 10^5 ( i = 1, 2, ..., Q )

Input

Input is given from Standard Input in the following format:

N M Q
a_1 b_1 c_1 d_1
:
a_Q b_Q c_Q d_Q

Output

Print the maximum possible score of A.

Sample Input 1

3 4 3
1 3 3 100
1 2 2 10
2 3 2 10

Sample Output 1

110

When A = \{1, 3, 4\}, its score is 110. Under these conditions, no sequence has a score greater than 110, so the answer is 110.

Sample Input 2

4 6 10
2 4 1 86568
1 4 0 90629
2 3 0 90310
3 4 1 29211
3 4 3 78537
3 4 2 8580
1 2 1 96263
1 4 2 2156
1 2 0 94325
1 4 3 94328

Sample Output 2

357500

Sample Input 3

10 10 1
1 10 9 1

Sample Output 3

1

Solution in JavaScript (Node.js 12.16.1) (judge verdict: Runtime Error)

function getCombArr(len = 2, comb = 1) {
  //10進数まで　重複を許す組み合わせ
  const num = Math.pow(len, comb),
    makeArr = (v, i) => {
      const n = i.toString(len),
        padStr = "0".repeat(comb - n.length);
      return (padStr + n).split("");
    };
  return [...Array(num).keys()].map(makeArr);
  //console.log(getCombArr(3, 2)); // [['0','0'],['0','1'],['0','2'],['1','0'],['1','1'],['1','2'],['2','0'],['2','1'],['2','2']]
}
function getCombArrNoSame(len = 2, comb = 1) {
  //重複を許さない組み合わせ
  const num = Math.pow(len, comb),
    makeArr = (v, i) => {
      const n = i.toString(len),
        padStr = "0".repeat(comb - n.length);
      return (padStr + n).split("");
    };
  const fil = (v, i) => {
    const n = v.toString(len),
      padStr = "0".repeat(comb - n.length);
    const arr = (padStr + n).split("").map((n) => parseInt(n, 10));
    var frag = true;
    for (var i = 1; i < arr.length; i++) {
      if (arr[i - 1] > arr[i]) {
        frag = false;
        break;
      }
    }
    return frag;
  };
  return [...Array(num).keys()].filter(fil).map(makeArr);
  //console.log(getCombArrNoSame(3, 2)); // [['0','0'],['0','1'],['0','2'],['1','1'],['1','2'],['2','2']]
}

// 上記関数を利用しつつ、組み合わせを作成
function getComb(arr = [], comb = 1) {
  const base = getCombArr(arr.length, comb),
    convert = (v) => arr[v],
    makeArr = (comb) => comb.map(convert);
  return base.map(makeArr);
  //console.log(getComb(['a', 'b', 'c'], 2));
  //     [ 'a', 'a' ],
  //     [ 'a', 'b' ],
  //     [ 'a', 'c' ],
  //     [ 'b', 'a' ],
  //     [ 'b', 'b' ],
  //     [ 'b', 'c' ],
  //     [ 'c', 'a' ],
  //     [ 'c', 'b' ],
  //     [ 'c', 'c' ]
  //   ]
}
// 上記関数を利用しつつ、組み合わせを作成
function getCombNoSame(arr = [], comb = 1) {
  const base = getCombArrNoSame(arr.length, comb),
    convert = (v) => arr[v],
    makeArr = (comb) => comb.map(convert);
  return base.map(makeArr);
  //console.log(getComb(['a', 'b', 'c'], 2));
  //     [ 'a', 'a' ],
  //     [ 'a', 'b' ],
  //     [ 'a', 'c' ],
  //     [ 'b', 'b' ],
  //     [ 'b', 'c' ],
  //     [ 'c', 'c' ]
  //   ]
}

function Main(input) {
  input = input.trim().split("\n");
  const NMQ = input[0].split(" ");
  var N = parseInt(NMQ[0], 10);
  var M = parseInt(NMQ[1], 10);
  var Q = parseInt(NMQ[2], 10);
  var a = [];
  var b = [];
  var c = [];
  var d = [];
  var aaa = [];
  var max = 0;

  for (var i = 0; i < Q; i++) {
    var abcd = input[i + 1].split(" ");
    a = a.concat(parseInt(abcd[0], 10));
    b = b.concat(parseInt(abcd[1], 10));
    c = c.concat(parseInt(abcd[2], 10));
    d = d.concat(parseInt(abcd[3], 10));
  }
  for (var i = 0; i < M; i++) {
    aaa = aaa.concat(i + 1);
  }
  var comb = getCombNoSame(aaa, N);

  for (var i = 0; i < comb.length; i++) {
    var score = 0;
    for (var q = 0; q < Q; q++) {
      if (comb[i][b[q] - 1] - comb[i][a[q] - 1] == c[q]) {
        score += d[q];
      }
    }
    if (score > max) {
      max = score;
    }
  }
  console.log(max);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));