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<iostream>
    #include<cstring>
    #include<cstdio>
    using namespace std;
    inline int read()
    {
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9')x=x*10+ch-'0',ch=getchar();
    return x*f;
    }
    int n,H,in[405],out[405],B[405],s[405],tote,size[405];
    inline int getfa(int x){return s[x]?s[x]=getfa(s[x]):x;}
    inline void Merge(int f,int t){if(getfa(f)!=getfa(t)) size[getfa(t)]+=size[getfa(f)],s[getfa(f)]=getfa(t);}
    int main()
    {
    n=read();H=read();
    for(int i=1;i<=n;++i)
    {
    int a=read(),b=read(),c=read(),d=read();
    int f=c?c+H:a,t=d?d:b+H;
    if(f==t) B[f]=1; else
    {
    ++out[f],++in[t];
    Merge(f,t);++size[getfa(f)];++tote;
    }
    // cout<<f<<" "<<t<<endl;
    }
    int S=0;
    for(int i=1;i<=H*2;++i)
    {
    // cout<<i<<" "<<in[i]<<" "<<out[i]<<endl;
    if(B[i]&&!in[i]&&!out[i]) return 0*puts("NO");
    if(i> H&&out[i]>in[i]) return 0*puts("NO");
    if(i<=H&&out[i]<in[i]) return 0*puts("NO");
    if(out[i]!=in[i])
    if(S) Merge(S,i);
    else S=i;
    }
    if(!S||size[getfa(S)]!=tote) return 0*puts("NO");
    puts("YES");
    return 0;
    }