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 <vector>
using std::vector;

#define MAXN 100005
#define MAXH 405
#define INF 1000000000
#define MOD 1000000007
int indeg[MAXH],outdeg[MAXH];
bool vis[MAXH];
vector<int> G[MAXH];

void add_edge(int u,int v)
{
    outdeg[u]++;indeg[v]++;
    G[u].push_back(v);G[v].push_back(u);
}

bool dfs(int v)
{
    bool f=indeg[v]!=outdeg[v];
    vis[v]=true;
    for(auto to:G[v])
	{
		if(!vis[to]) 
			f|=dfs(to);
	}
    return f;
}

int main()
{
	int N,H;
	int a[MAXN],b[MAXN],c[MAXN],d[MAXN];
    scanf("%d%d",&N,&H);
    for(int i=1;i<=N;i++) 
    {
        scanf("%d%d%d%d",&a[i],&b[i],&c[i],&d[i]);
        int l,r;
		l= ( c[i]==0 ? a[i] : -c[i] );
        r= ( d[i]==0 ? -b[i] : d[i] );
        add_edge(l+H,r+H);
    }

    bool flag=true;
    for(int i=0;flag && i<=H;i++) 
	{
		if(outdeg[i]>indeg[i]) 
			flag=false;
	}
    for(int i=H+1;flag && i<=2*H;i++)
	{
		if(indeg[i]>outdeg[i]) 
	 		flag=false;
	}

    memset(vis,false,sizeof(vis));
    for(int i=0;flag && i<=2*H;i++)
	{
		if((indeg[i]||outdeg[i])&&!vis[i]) 
			flag &=dfs(i);
	}

    if(flag) 
	{
		printf("YES\n"); 
	}
	else
	{ 
		printf("NO\n");
	}
    return 0;
}
