We have N irregular jigsaw pieces. Each piece is composed of three rectangular parts of width 1 and various heights joined together. More specifically:

* The i-th piece is a part of height H, with another part of height A_i joined to the left, and yet another part of height B_i joined to the right, as shown below. Here, the bottom sides of the left and right parts are respectively at C_i and D_i units length above the bottom side of the center part.



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Snuke is arranging these pieces on a square table of side 10^{100}. Here, the following conditions must be held:

* All pieces must be put on the table.
* The entire bottom side of the center part of each piece must touch the front side of the table.
* The entire bottom side of the non-center parts of each piece must either touch the front side of the table, or touch the top side of a part of some other piece.
* The pieces must not be rotated or flipped.



Determine whether such an arrangement is possible.

Constraints

* 1 \leq N \leq 100000
* 1 \leq H \leq 200
* 1 \leq A_i \leq H
* 1 \leq B_i \leq H
* 0 \leq C_i \leq H - A_i
* 0 \leq D_i \leq H - B_i
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N H
A_1 B_1 C_1 D_1
A_2 B_2 C_2 D_2
:
A_N B_N C_N D_N


Output

If it is possible to arrange the pieces under the conditions, print `YES`; if it is impossible, print `NO`.

Examples

Input

3 4
1 1 0 0
2 2 0 1
3 3 1 0


Output

YES


Input

4 2
1 1 0 1
1 1 0 1
1 1 0 1
1 1 0 1


Output

NO


Input

10 4
1 1 0 3
2 3 2 0
1 2 3 0
2 1 0 0
3 2 0 2
1 1 3 0
3 2 0 0
1 3 2 0
1 1 1 3
2 3 0 0


Output

YES
#include <iostream>
#include <cstring>
#include <vector>
using namespace std;
int N, H;
int LD[205], RD[205], LU[205], RU[205];
int Out[405], In[405], Use[405], ok;
vector <int> G[405];
const int add = 201;
void Read()
{
    cin >> N >> H;
    for(int i = 1; i <= N; i++)
    {
        int a, b, c, d;
        cin >> a >> b >> c >> d;
        int l, r;
        if(c > 0)
        {
            l = -c;
        }
        else
            l = a;
        if(d > 0)
        {
            r = d;
        }
        else
            r = -b;
        G[l + add].push_back(r + add);
        G[r + add].push_back(l + add);
        In[r + add]++;
        Out[l + add]++;
    }
}

void DFS(int node)
{
    Use[node] = 1;
    if(In[node] != Out[node])
    {
        ok = 1;
    }
    for(int i = 0; i < G[node].size(); i++)
    {
        int neighb = G[node][i];
        if(Use[neighb] == 0)
            DFS(neighb);
    }
}
int main()
{
    Read();
    for(int i = 1; i <= 402; i++)
        if(Use[i] == 0 && G[i].size() > 0)
        {
            ok = 0;
            DFS(i);
            if(ok == 0)
            {
                cout << "NO\n";
                return 0;
            }
        }
    for(int i = 1; i <= 402; i++)
    {
        if(i < add && In[i] < Out[i])
        {
            cout << "NO\n";
            return 0;
        }
        if(i > add && In[i] > Out[i])
        {
            cout << "NO\n";
            return 0;
        }

    }
    cout << "YES\n";
    return 0;
}
