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;

class UF {
  vector<int> ps;
public:
  void init(int n) {
    ps.resize(n);
    for (int i = 0; i < n; ++i) {
      ps[i] = i;
    }
  }
  int root(int i) {
    if (ps[i] == i) return i;
    return ps[i] = root(ps[i]);
  }
  bool same(int i, int j) {
    return root(i) == root(j);
  }
  void unite(int i, int j) {
    if (i == j) return;
    int ri = root(i);
    int rj = root(j);
    ps[ri] = rj;
  }
};

int n, h;
int deg[403];
bool iso[403];
UF uf;
bool sub() {
  for (int i = 0; i < 2 * h; ++i) {
    if (i < h && deg[i] < 0) return false;
    if (i >= h && deg[i] > 0) return false;
  }
  
  vector<vector<int>> gs(2 * h);
  for (int i = 0; i < 2 * h; ++i) {
    gs[uf.root(i)].push_back(i);
  }
  
  for (auto&& g : gs) {
    if (g.empty() || iso[g[0]]) continue;
    int sum = 0;
    bool ok = false;
    for (int i : g) {
      sum += deg[i];
      if (deg[i] != 0) ok = true;
    }
    if (!ok || sum != 0) return false;
  }
  return true;
}

int main() {
  cin >> n >> h;
  ++h;
  uf.init(2 * h);
  
  for (int i = 0; i < 2 * h; ++i) {
    iso[i] = true;
  }
  
  for (int i = 0; i < n; ++i) {
    int a, b, c, d;
    cin >> a >> b >> c >> d;
    
    int x = c == 0 ? a : c + h;
    int y = d == 0 ? b + h : d;
    ++deg[x];
    --deg[y];
    iso[x] = false;
    iso[y] = false;
    uf.unite(x, y);
  }
  
  cout << (sub() ? "YES" : "NO") << endl;
}