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 <cmath>
#include <cstdio>
#include <vector>
using namespace std;
const int M = 1e5 + 10;
int f[600] , cnt[600] , c[600];
vector<int>vc[600];
void init() {
    for(int i = 0 ; i <= 555 ; i++) {
        cnt[i] = 0;
        c[i] = 0;
        f[i] = i;
    }
}
int find(int x) {
    if(x == f[x]) return x;
    int tmp = find(f[x]);
    return f[x] = tmp;
}

int main() {
    int n , h;
    scanf("%d%d" , &n , &h);
    init();
    for(int i = 1 ; i <= n ; i++) {
        int a , b , c , d;
        scanf("%d%d%d%d" , &a , &b , &c , &d);
        int x = c , y = -d;
        if(c == 0) x = -a;
        if(d == 0) y = b;
        x += 250 , y += 250;
        vc[x].push_back(y);
        cnt[x]++ , cnt[y]--;
        f[find(x)] = find(y);
    }
    int flag = 1;
    for(int i = 0 ; i <= 500 ; i++) {
        if(i > 250 && cnt[i] > 0) flag = 0;
        if(i < 250 && cnt[i] < 0) flag = 0;
        if(cnt[i] > 0) {
            c[find(i)] = 1;
        }
    }
    for(int i = 0 ; i <= 500 ; i++) {
        if(vc[i].size() > 0 && !c[find(i)]) flag = 0;
    }
    flag ? puts("YES") : puts("NO");
    return 0;
}