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<bits/stdc++.h>

using namespace std;

int N, H, balance[409];
vector < int > v[409];

void answer (bool value)
{
    if (value) printf ("YES\n");
    else printf ("NO\n");
    exit (0);
}

bool anyNonZero, anyEdge, ap[409], anyLoop[409];
void dfs (int nod)
{
    ap[nod] = 1, anyNonZero |= (balance[nod] != 0);
    anyEdge |= anyLoop[nod];
    for (auto it : v[nod])
        if (ap[it] == 0)
            dfs (it), anyEdge = 1;
}

int main ()
{
//freopen ("input", "r", stdin);
//freopen ("output", "w", stdout);

scanf ("%d %d", &N, &H);
for (int i=1; i<=N; i++)
{
    int a, b, c, d, x, y;
    scanf ("%d %d %d %d", &a, &b, &c, &d);
    x = (c == 0 ? H + a + 1 : c);
    y = (d != 0 ? H + d + 1 : b);
    v[x].push_back (y);
    v[y].push_back (x);
//    printf ("%d -> %d\n", x, y);
    balance[x] ++, balance[y] --;
    if (x == y) anyLoop[x] = 1;
}
for (int i=1; i<=2 * H; i++)
    if ((balance[i] > 0 && i <= H) ||
        (balance[i] < 0 && i > H))
            answer (0);
for (int i=1; i<=2 * H; i++)
    if (ap[i] == 0)
    {
        anyNonZero = 0;
        anyEdge = 0;
        dfs (i);
        if (!anyNonZero && anyEdge)
            answer (0);
    }
answer (1);
return 0;
}
