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>
#define ll long long
#define For(i,a,b) for (int i=a;i<=b;i++)
#define Rep(i,a,b) for (int i=b;i>=a;i--)
#define N 2000500
using namespace std;
int n,m,fa[N],vis[N],D[N],C[N];
int gf(int x) {return fa[x]==x?x:fa[x]=gf(fa[x]);}
inline ll read()
{
    ll 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 main() 
{
    n = read(), m = read();
	For(i,1,1000)fa[i] = i;
    For(i,1,n)
	{
        int x, y,a,b,c,d;
        a = read(), b = read(), c = read(), d = read();
        x=!c?a:-c; x+=500;
        y=!d?-b:d; y+=500;
        fa[ gf(x) ] = gf(y);
        D[x]++, D[y]--, vis[x] = 1;
    }
    int flag = 1;
	For(i,1,499)D[i]>0 ? flag=0 :0;
	For(i,501,1000)D[i]<0 ? flag=0 :0;
	For(i,1,1000)vis[gf(i)] |= vis[i];
    For(i,1,1000) if (D[i]) C[gf(i)] = 1;
    For(i,1,1000) if (fa[i]==i && !C[i] && vis[i]) flag = 0;
    puts(flag?"YES":"NO");
    return 0;
}