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.



<image>

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;

void err() {
  puts("NO");
  exit(0);
}

const int MAX = 410;
const int K = 200;

vector <int> _g[2 * MAX], _gr[2 * MAX], *g = _g + MAX, *gr = _gr + MAX;
int _x[2 * MAX], _din[2 * MAX], _dout[2 * MAX], *x = _x + MAX, *din = _din + MAX, *dout = _dout + MAX;
bool _was[2 * MAX], *was = _was + MAX;

int main() {
  int n, h;
  scanf("%d %d", &n, &h);
  for (int i = 0; i < n; i++) {
    int a, b, c, d;
    scanf("%d %d %d %d", &a, &b, &c, &d);
    int x = (c == 0 ? -a : c);
    int y = (d == 0 ? b : -d);
    g[x].push_back(y);
    gr[y].push_back(x);
  }
  for (int i = -K; i <= K; i++) {
    dout[i] = g[i].size();
    din[i] = gr[i].size();
    if (i < 0 && dout[i] < din[i]) {
      err();
    }
    if (i > 0 && dout[i] > din[i]) {
      err();
    }
    was[i] = (din[i] + dout[i] == 0 ? true : false);
  }
  for (int i = -K; i <= K; i++) {
    if (was[i]) {
      continue;
    }
    int b = 0, e = 1;
    x[0] = i;
    was[i] = true;
    while (b < e) {
      for (int j : g[x[b]]) {
        if (!was[j]) {
          was[j] = true;
          x[e++] = j;
        }
      }
      for (int j : gr[x[b]]) {
        if (!was[j]) {
          was[j] = true;
          x[e++] = j;
        }
      }
      b++;
    }
    int sum_pos = 0, sum_neg = 0;
    for (int j = 0; j < e; j++) {
      if (x[j] > 0) {
        sum_pos += din[x[j]] - dout[x[j]];
      } else {
        sum_neg += dout[x[j]] - din[x[j]];
      }
    }
    if (sum_pos != sum_neg || sum_pos == 0) {
      err();
    }
  }
  puts("YES");
  return 0;
}
