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 <iostream>
#include <algorithm>
using namespace std;
const int Q=1<<20;
int fa[Q];
int in[Q],out[Q];
int gf(int x)
{return fa[x]==x?x:(fa[x]=gf(fa[x]));}
void ins(int x,int y)
{
    out[x]++;
    in[y]++;
    int fx=gf(x),fy=gf(y);
    if(fx!=fy)fa[fx]=fy;
}
// int Idiot_Sap(int x,int flow)
// {
//     if(x==T)return flow;
//     int had=0;
//     for(int t=las[x];t;t=nn[t]){
//         int y=e[t];
//         if((!c[t])||dis[x]-1!=dis[y])continue;
//         int del=Idiot_Sap(y,min(c[t],flow-had));
//         c[t]-=del;
//         c[t^1]+=del;
//         had+=del;
//         if(dis[S]>=T||had==flow)return had;
//     }
//     if(dis[S]>=T)return had;
//     --cnt[dis[x]];
//     if(!cnt[dis[x]])dis[S]=T;
//     cnt[++dis[x]]++;
//     return had;
// }
int had[Q];
int main()
{
    int n,h;
    cin>>n>>h;
    h+=5;
    for(int i=1;i<=h+h;i++)fa[i]=i;
    for(int i=1,a,b,c,d;i<=n;i++){
        scanf("%d%d%d%d",&a,&b,&c,&d);
        ++a,++b,++c,++d;
        int x,y;
        if(c==1)x=a+h;
        else x=c;
        if(d==1)y=b;
        else y=d+h;
        // printf("%d %d LINK\n",x,y);
        ins(x,y);
    }
    for(int i=1;i<=h;i++)if(out[i]>in[i])return puts("NO")&0;
    for(int i=h+1;i<=h+h;i++)if(out[i]<in[i])return puts("NO")&0;
    for(int i=1;i<=h+h;i++)if(in[i]!=out[i])had[gf(i)]=1;
    for(int i=1;i<=h+h;i++)if(in[i]&&out[i]&&(!had[gf(i)]))return puts("NO")&0;
    puts("YES");
    return 0;
}