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 <cstdio>
#include <algorithm>
#include <vector>

using namespace std;

vector <int> v[512];
int in[512], out[512], trec[512];

#define v (v + 230)
#define trec (trec + 230)
#define in (in + 230)
#define out (out + 230)

bool OK;

void dfs (int nod)
{
    trec[nod] = 1;
    if (in[nod] != out[nod]) OK = true;

    for (auto &it : v[nod])
        if (!trec[it]) dfs (it);
}

int main ()
{
   // freopen ("file.in", "r", stdin);

    int n, h;
    scanf ("%d %d", &n, &h);

    for (int i = 1; i <= n; ++i)
    {
        int a, b, c, d, l, r;
        scanf ("%d %d %d %d", &a, &b, &c, &d);

        if (!c) l = a;
        else l = -c;

        if (!d) r = -b;
        else r = d;

        v[l].push_back (r);
        v[r].push_back (l);

        ++out[l];
        ++in[r];
    }

    for (int i = -h; i <= h; ++i)
    {
        if (i < 0)
        {
            if (in[i] < out[i])
            {
                printf ("NO\n");
                return 0;
            }
        }

        if (i > 0)
        {
            if (in[i] > out[i])
            {
                printf ("NO\n");
                return 0;
            }
        }
    }

    trec[0] = 1;

    for (int i = -h; i <= h; ++i)
        if (!trec[i] && (in[i] || out[i]))
        {
            OK = false;
            dfs (i);

            if (!OK)
            {
                printf ("NO\n");
                return 0;
            }
        }

    printf ("YES\n");

    return 0;
}
