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 <cstring>
#include <cctype>
using namespace std;
inline int read(int f = 1, int x = 0, char ch = ' ')
{
    while(!isdigit(ch = getchar())) if(ch == '-') f = -1;
    while(isdigit(ch)) x = x*10+ch-'0', ch = getchar();
    return f*x;
}
const int N = 400+5;
int n, h, in[N], out[N], fa[N], valid[N];
int find(int x) { return fa[x] == x?x:fa[x] = find(fa[x]); }
int main()
{
    n = read(), h = read();
    for(int i = 1; i <= h<<1; ++i) fa[i] = i; 
    for(int i = 1; i <= n; ++i)
    {
        int a = read(), b = read(), c = read(), d = read();
        int x = c?c+h:a, y = d?d:b+h;
        ++out[x], ++in[y], x = find(x), y = find(y), fa[x] = y;
    }
    for(int i = 1; i <= h; ++i) if(in[i] > out[i]) return puts("NO"), 0;
    for(int i = h+1; i <= h<<1; ++i) if(in[i] < out[i]) return puts("NO"), 0;
    for(int i = 1; i <= h<<1; ++i) if(in[i] != out[i]||!in[i]) valid[find(i)] = 1;
    for(int i = 1; i <= h<<1; ++i) if(find(i) == i&&!valid[i]) return puts("NO"), 0;
    puts("YES");
    return 0;
}