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 <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <cassert>
using namespace std;
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;
const ll mod=1000000007;
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
// head

const int N=1010;
int n,h,f[N],deg[N],vis[N];
int find(int x) { return f[x]==x?x:f[x]=find(f[x]); }
int a,b,c,d;
void add(int pl,int pr) {
	deg[pl]--; deg[pr]++;
	vis[pl]=vis[pr]=1;
	f[find(pl)]=find(pr);
}
int main() {
	scanf("%d%d",&n,&h);
	rep(i,0,2*h+2) f[i]=i;
	rep(i,0,n) {
		scanf("%d%d%d%d",&a,&b,&c,&d);
		int pl=(c==0)?a:c+h+1;
		int pr=(d==0)?b+h+1:d;
		add(pl,pr);
	}
	rep(i,0,h+1) if (deg[i]>0) {
		puts("NO");
		return 0;
	}
	rep(i,h+1,2*h+2) if (deg[i]<0) {
		puts("NO");
		return 0;
	}
	rep(i,0,h+1) if (vis[i]) {
		bool val=0;
		rep(j,0,2*h+2) if (find(i)==find(j)&&deg[j]<0) val=1;
		if (!val) { puts("NO"); return 0;}
	}
	rep(i,h+1,2*h+2) if (vis[i]) {
		bool val=0;
		rep(j,0,2*h+2) if (find(i)==find(j)&&deg[j]>0) val=1;
		if (!val) { puts("NO"); return 0;}
	}
	puts("YES");
}
