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 <cstdio>
#include <numeric>

const int N = 400 + 10;

int n, deg[N];

int anc[N], cnt[N], mask[N];

int find(int x) { return anc[x] == x ? x : (anc[x] = find(anc[x])); }

void init() {
  int m;
  scanf("%d%d", &m, &n);
  std::iota(anc, anc + 2 * n + 1, 0);
  while (m--) {
    int a, b, c, d;
    scanf("%d%d%d%d", &a, &b, &c, &d);
    int x = c ? (c + n) : a, y = d ? d : (b + n);
    ++cnt[x], ++cnt[y];
    --deg[x], ++deg[y];
    anc[find(x)] = find(y);
  }
}

int main() {
  init();
  for (int i = 1; i <= n; ++i) if (deg[i] > 0 || deg[i + n] < 0) return puts("NO"), 0;
  for (int i = 1; i <= 2 * n; ++i) mask[find(i)] |= deg[i];
  for (int i = 1; i <= 2 * n; ++i) if (find(i) == i && cnt[i] && !mask[i]) return puts("NO"), 0;
  puts("YES");
  return 0;
}
