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: Time Limit Exceeded)

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define pb push_back
#define mp make_pair
#define F first
#define S second
ll int q[55][10];
ll int N,M;
ll int fun(vector<ll int> x,ll int i)
{
    //cout<<M<<endl;
    //cout<<i<<endl;
    ll int a,b,c,d,j,z;
    a=q[i][0];b=q[i][1];c=q[i][2];d=q[i][3];
    a-=1;b-=1;
    if(i==0)
    {
        ll int mx,mn,mn1,mx1;
        if(x[b]==-1&&x[a]==-1)
        {
            mx=M;
            mn=1;
            mx1=1;
            mn1=M;
            ll int maxi=0;
            for(j=b+1;j<N;j++)
            {
                if(x[j]!=-1)
                {
                    mx=x[j];
                    break;
                }
            }    
            for(j=a-1;j>=0;j--)
            {
                if(x[j]!=-1)
                {
                    mn=x[j];
                    break;
                }
            }
            for(j=b-1;j>=0;j--)
            {
                if(x[j]!=-1)
                {
                    mx1=x[j];
                    break;
                }
            }
            for(j=a+1;j<N;j++)
            {
                if(x[j]!=-1)
                {
                    mn1=x[j];
                    break;
                }
            }
            for(j=mx;j>=mn;j--)
            {
                if(j>=mx1&&(j-c)>=mn&&(j-c)<=mn1)
                {
                   x[b]=j;
                   x[a]=j-c;
                   maxi=d;
                }
            }
            return maxi;
        }
        else if(x[b]!=-1&&x[a]==-1)
        {
            mn=1;
            mn1=M;
            for(j=a-1;j>=0;j--)
            {
                if(x[j]!=-1)
                {
                    mn=x[j];
                    break;
                }
            }
            for(j=a+1;j<N;j++)
            {
                if(x[j]!=-1)
                {
                    mn1=x[j];
                    break;
                }
            }
            if((x[b]-c)>=mn&&(x[b]-c)<=mn1)
            return d;
            else
            return 0;
        }
        else if(x[b]==-1&&x[a]!=-1)
        {
            mx=M;
            mx1=1;
            for(j=b+1;j<N;j++)
            {
                if(x[j]!=-1)
                {
                    mx=x[j];
                    break;
                }
            }
            for(j=b-1;j>=0;j--)
            {
                if(x[j]!=-1)
                {
                    mx1=x[j];
                    break;
                }
            }
            if((x[a]+c)<=mx&&(x[a]+c)>=mx1)
            return d;
            else
            return 0;
        }
        else
        {
            if((x[b]-x[a])==c)
            return d;
            else
            return 0;
        }
    }
    else
    {
        ll int mx,mn,mn1,mx1;
        ll int p=fun(x,i-1);
        //cout<<i<<endl;
        //for(auto l=0;l<N;l++)
        //cout<<x[l]<<" ";
        //cout<<endl;
        if((x[b]==-1)&&(x[a]==-1))
        {
            //cout<<" hm yha aayye inke liye "<<i<<endl;
            ll int maxi;
            mx=M;
            mn=1;
            mn1=M;
            mx1=1;
            maxi=0;
            for(j=b+1;j<N;j++)
            {
                if(x[j]!=-1)
                {
                    mx=x[j];
                    break;
                }
            }
            for(j=a-1;j>=0;j--)
            {
                if(x[j]!=-1)
                {
                    mn=x[j];
                    break;
                }
            }
            for(j=a+1;j<N;j++)
            {
                if(x[j]!=-1)
                {
                    mn1=x[j];
                    break;
                }
            }
            for(j=b-1;j>=0;j--)
            {
                if(x[j]!=-1)
                {
                    mx1=x[j];
                    break;
                }
            }
            for(j=mx;j>=mn;j--)
            {
                if(j>=mx1&&(j-c)>=mn&&(j-c)<=mn1)
                {
                   x[b]=j;
                   x[a]=j-c;
                   z=d+fun(x,i-1);
                   maxi=maxi>=z?maxi:z;
                }
            }
            return maxi>=p?maxi:p;
        }
        else if(x[b]!=-1&&x[a]==-1)
        {
            mn=1;
            mn1=M;
            for(j=a-1;j>=0;j--)
            {
                if(x[j]!=-1)
                {
                    mn=x[j];
                    break;
                }
            }
            for(j=a+1;j<N;j++)
            {
                if(x[j]!=-1)
                {
                    mn1=x[j];
                    break;
                }
            }
            if((x[b]-c)>=mn&&(x[b]-c)<=mn1)
            {
                x[a]=x[b]-c;
                ll int t=fun(x,i-1);
                return (d+t)>=p?(d+t):p;
            }
            else
            {
                return p;
            }
        }
        else if(x[b]==-1&&x[a]!=-1)
        {
            mx=M;
            mx1=1;
            for(j=b+1;j<N;j++)
            {
                if(x[j]!=-1)
                {
                    mx=x[j];
                    break;
                }
            }
            for(j=b-1;j>=0;j--)
            {
                if(x[j]!=-1)
                {
                    mx1=x[j];
                    break;
                }
            }
            if((x[a]+c)<=mx&&(x[a]+c)>=mx1)
            {
                x[b]=x[a]+c;
                ll int t=fun(x,i-1);
                return (d+t)>=p?(d+t):p;
            }
            else
            return p;
        }
        else
        {
            if((x[b]-x[a])==c)
                return d+p;
            else
                return p;
        }
    }
}
int main()
{
    ll int x[15],i,j,Q;
    vector<ll int> v;
    cin>>N>>M>>Q;
    for(i=0;i<Q;i++)
    {
        for(j=0;j<4;j++)
        {
            cin>>q[i][j];
        }
    }
    
    for(i=0;i<15;i++)
    {
        v.pb(-1);
    }
    cout<<fun(v,Q-1);
    return 0;
}