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<bits/stdc++.h>
using namespace std;
#define N 100005
#define M 205
vector<int> g[N];
bool vis[N],chk[N];
int du[N];//outd - ind
void addedge(int f,int t){
    f+=M,t+=M;
    chk[f]=chk[t]=true;
    g[f].push_back(t);
    g[t].push_back(f);
    du[f]++,du[t]--;
}
bool DFS(int u){
    bool ret= du[u]!=0 ;vis[u]=true;
    for(int i:g[u])  
        if(!vis[i]) ret|=DFS(i);
    return ret;
}
int n,h;
int main(){
    scanf("%d%d",&n,&h);
    for(int i=1,a,b,c,d;i<=n;i++){
        scanf("%d%d%d%d",&a,&b,&c,&d);
        addedge((c==0? a:-c),(d==0? -b:d) );
    }
    for(int i=-h;i<=h;i++)
        if(i!=0&&i*du[i+M]<0)
            return puts("NO"),0;
    for(int i=-h;i<=h;i++)
        if(chk[i+M]&&i!=0&&!vis[i+M]&&!DFS(i+M))
            return puts("NO"),0;
    return puts("YES"),0;
}