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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

int N, M, Q;

void zeroclear(int *p);
void oneclear(int *p);
void of(int *p);
int hadd(const int *p);
void genA(const int *ind, int *As);

int main(void)
{
    int cc, score = 0, temp;
    int *a, *b, *c, *d, *ind, *As;
    scanf("%d %d %d", &N, &M, &Q);
    a = (int *)malloc(sizeof(int) * Q);
    b = (int *)malloc(sizeof(int) * Q);
    c = (int *)malloc(sizeof(int) * Q);
    d = (int *)malloc(sizeof(int) * Q);
    ind = (int *)malloc(sizeof(int) * N);
    As = (int *)malloc(sizeof(int) * N);
    zeroclear(ind);
    oneclear(As);
    for (cc = 0; cc < Q; ++cc)
    {
        scanf("%d %d %d %d", a + cc, b + cc, c + cc, d + cc);
    }
    while (1)
    {
        temp = 0;
        genA(ind, As);
        if (ind[N - 1] > M)
        {
            break;
        }
        for (cc = 0; cc < Q; ++cc)
        {
            if (As[b[cc] - 1] - As[a[cc] - 1] == c[cc])
            {
                temp += d[cc];
            }
        }
        if (temp > score)
        {
            score = temp;
        }
        ++ind[0];
        if (hadd(ind) > M)
        {
            ind[0] += M + 1;
        }
        of(ind);
    }
    printf("%d", score);
    free(a);
    free(b);
    free(c);
    free(d);
    return 0;
}

void zeroclear(int *p)
{
    int cc;
    for (cc = 0; cc < N; ++cc)
    {
        p[cc] = 0;
    }
}

void oneclear(int *p)
{
    int cc;
    for (cc = 0; cc < N; ++cc)
    {
        p[cc] = 1;
    }
}

void of(int *p)
{
    int cc;
    for (cc = 0; cc < N - 1; ++cc)
    {
        if (p[cc] > M)
        {
            p[cc] = 0;
            ++p[cc + 1];
        }
    }
}

int hadd(const int *p)
{
    int cc, ans = 0;
    for (cc = 0; cc < N; ++cc)
    {
        ans += p[cc];
    }
    return ans;
}

void genA(const int *ind, int *As)
{
    int cc;
    oneclear(As);
    As[0] += ind[0];
    for (cc = 1; cc < N; ++cc)
    {
        As[cc] = As[cc - 1];
        As[cc] += ind[cc];
    }
}