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 <cctype>
#include <algorithm>
#define repu(i,x,y) for (int i=x; i<=y; ++i)
using namespace std;

int n,h,deg[410],cnt;
bool flag[410];
struct edge
{
    int v;
    edge *nxt;
} pool[100100],*tp=pool,*fst[410];

int getint()
{
    char ch;
    while (!isdigit(ch=getchar()));
    int x=ch-'0';
    for (; isdigit(ch=getchar()); x=x*10+ch-'0');
    return x;
}

void addedge(int u,int v)
{
    *tp=(edge){v,fst[u]},fst[u]=tp++;
    ++deg[u],--deg[v];
}

void dfs(int x)
{
    if (flag[x])
        return;
    flag[x]=1;
    for (edge *i=fst[x]; i; i=i->nxt)
        ++cnt,dfs(i->v);
}

bool check()
{
    repu(i,1,n)
    {
        int a=getint(),b=getint(),c=getint(),d=getint();
        int u=c?c:h+a,v=d?h+d:b;
        addedge(u,v);
    }
    repu(i,1,h*2)
    {
        if (deg[i]>0)
            if (i>h)
                dfs(i);
            else
                return 0;
        if (deg[i]<0 && i>h)
            return 0;
    }
    return cnt==n;
}

int main()
{
    scanf("%d%d",&n,&h);
    puts(check()?"YES":"NO");
    return 0;
}