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
#pragma comment(linker,"/STACK:1000000000")
#include<iostream>
#include<algorithm>
#include<vector>
#include<set>
using namespace std;

#define sz(x) (int)(x.size())
#define fi(a,b) for(int i=a;i<b;++i)
#define fj(a,b) for(int j=a;j<b;++j)
#define fo(a,b) for(int o=a;o<b;++o)
#define pb push_back
#define mp make_pair
typedef pair<int, int> pii;
////////////////////

int const N = 1e5 + 41;
int const H = 241;

int n, h, a[N], b[N], c[N], d[N];
int deg[H][2], d0[H][2], d1[H][2];
int w[N][2];
vector<pii> e[H][2];

pii getfrom(int a, int c){
	if(c == 0) return mp(a, 1);
	else return mp(c, 0);
}

pii getto(int b, int d){
	if(d > 0) return mp(d, 1);
	else return mp(b, 0);
}

void bad(){
	printf("NO\n");
	exit(0);
}

void dfs(pii x){
	w[x.first][x.second] = 1;
	fi(0, sz(e[x.first][x.second])){
		pii y = e[x.first][x.second][i];
		if(!w[y.first][y.second]) dfs(y);
	}
}

void solve(){
	fi(0, n){
		pii x = getfrom(a[i], c[i]);
		pii y = getto(b[i], d[i]);
		e[x.first][x.second].pb(y);
		++deg[x.first][x.second];
		--deg[y.first][y.second];
	}
	fi(1, h+1) fj(0, 2){
		if(j == 1){
			if(deg[i][j] < 0) bad();
		}else{
			if(deg[i][j] > 0) bad();
		}
	}
	fi(1, h+1) if(deg[i][1] > 0) dfs(mp(i, 1));
	fi(1, h+1) fj(0, 2) if(sz(e[i][j]) > 0 && !w[i][j]) bad();
}

int main(){
#ifdef _DEBUG
	freopen("input.txt","r",stdin);
	freopen("output.txt","w",stdout);
#endif
	
	scanf("%d %d",&n,&h);
	fi(0, n) scanf("%d %d %d %d",&a[i],&b[i],&c[i],&d[i]);

	solve();

	printf("YES\n");

	return 0;
}