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>

void bye() { std::cout << "NO" << std::endl; exit(0); }
int ind[410], oud[410], fa[410], idx;
int p[210][2], hav[410];
int n, H;
int find(int x) { return x == fa[x] ? x : fa[x] = find(fa[x]); }
int newnode() { ++idx; fa[idx] = idx; return idx; }
int get(int x, int b) { return p[x][b] ? p[x][b] : p[x][b] = newnode(); }
void adde(int b, int e) { ++ind[e], ++oud[b]; fa[find(b)] = find(e); }
int main() {
	std::ios_base::sync_with_stdio(false), std::cin.tie(0);
	std::cin >> n >> H;
	for (int i = 1; i <= n; ++i) {
		int a, b, c, d;
		std::cin >> a >> b >> c >> d;
		adde(c ? get(c, 1) : get(a, 0), d ? get(d, 0) : get(b, 1));
	}
	for (int i = 1; i <= H; ++i) {
		if (int t = p[i][0]) {
			if (ind[t] > oud[t]) bye(); hav[find(t)] |= ind[t] != oud[t];
		}
		if (int t = p[i][1]) {
			if (ind[t] < oud[t]) bye(); hav[find(t)] |= ind[t] != oud[t];
		}
	}
	for (int i = 1; i <= idx; ++i) if (fa[i] == i && !hav[i]) bye();
	std::cout << "YES" << std::endl;
	return 0;
}
