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<set>
#include<map>
#include<deque>
#include<queue>
#include<stack>
#include<cmath>
#include<ctime>
#include<bitset>
#include<string>
#include<vector>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<climits>
#include<complex>
#include<iostream>
#include<algorithm>
#define ll long long
using namespace std;

const int maxn = 410000;

int n,m=800;

int fa[maxn];
int findfa(const int x){return fa[x]==x?x:fa[x]=findfa(fa[x]);}

int d[maxn],v[maxn],ok[maxn];

int main()
{
    scanf("%d%*d",&n);
    for(int i=1;i<m;i++) fa[i]=i;
    for(int i=1;i<=n;i++)
    {
        int a,b,c,D,l,r; scanf("%d%d%d%d",&a,&b,&c,&D);
        l=!c?a:-c;
        r=!D?-b:D;
        l+=400,r+=400;
        d[l]++,d[r]--; v[l]=v[r]=1;
        fa[findfa(l)]=findfa(r);
    }
    for(int i=1;i<=400;i++) if(d[i]>0) return puts("NO"),0;
    for(int i=400;i<m;i++)  if(d[i]<0) return puts("NO"),0;

    for(int i=1;i<m;i++) if(d[i]) ok[findfa(i)]=1;

    for(int i=1;i<m;i++) if(i==findfa(i)&&v[i]&&!ok[i]) 
        return puts("NO"),0;
    puts("YES");

    return 0;
}