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 <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

const int N = 500;

int n, h;
int in[N], out[N], fa[N];
bool self[N];

inline int getf(int x) {
  return fa[x] ? fa[x] = getf(fa[x]) : x;
}

inline void link(int x, int y) {
  x = getf(x); y = getf(y);
  if (x != y) fa[x] = y;
}

int main() {
  scanf("%d%d", &n, &h);
  for (int i = 1, a, b, c, d, p, q; i <= n; i ++) {
    scanf("%d%d%d%d", &a, &b, &c, &d);
    if (!c) p = h + a;
    else p = h - c;
    if (!d) q = h - b;
    else q = h + d;
    link(p, q);
    out[p] ++; in[q] ++;
    if (p == q) self[p] = 1;
    // cerr << p << " "<< q << endl;
  }
  for (int i = 0; i <= h + h; i ++) {
    if (i > h && in[i] > out[i]) return 0 * puts("NO");
    if (i < h && in[i] < out[i]) return 0 * puts("NO");
    bool fd = 0, fri = self[i];
    for (int j = 0; j <= h + h && !fd; j ++)
      if (getf(j) == getf(i)) {
        if (i != j) fri = 1;
        if (in[j] != out[j]) fd = 1;
      }
  if (!fd && fri) return 0 * puts("NO");
  }
  puts("YES");
  return 0;
}
