p03669 AtCoder Grand Contest 017 - Jigsaw
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.



<image>

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
```python
import sys
from collections import Counter

# sys.stdin = open('e1.in')


def read_int_list():
    return list(map(int, input().split()))


def read_int():
    return int(input())


def read_str_list():
    return input().split()


def read_str():
    return input()


total_in = 0
total_out = 0


def solve():
    n, h = read_int_list()
    a, b, c, d = zip(*[read_int_list() for _ in range(n)])
    n_nodes = 2 * h + 1
    n_edges = n
    adj = [[] for _ in range(n_nodes)]
    r_adj = [[] for _ in range(n_nodes)]
    for i in range(n_edges):
        if c[i] == 0:
            l = a[i]
        else:
            l = -c[i]
        if d[i] == 0:
            r = -b[i]
        else:
            r = d[i]
        adj[l + h].append(r + h)
        r_adj[r + h].append(l + h)
    in_degree = Counter()
    out_degree = Counter()
    for i in range(n_nodes):
        for j in adj[i]:
            out_degree[i] += 1
            in_degree[j] += 1

    for i in range(n_nodes):
        if i < h:
            if not out_degree[i] <= in_degree[i]:
                return 'NO'
        if h < i:
            if not in_degree[i] <= out_degree[i]:
                return 'NO'

    state = [0] * n_nodes

    def dfs(root):
        res = False
        state[root] = 1
        for i in adj[root]:
            if state[i] == 0:
                res |= dfs(i)
        for i in r_adj[root]:
            if state[i] == 0:
                res |= dfs(i)
        state[root] = 2
        if (in_degree[root], out_degree[root]) == (0,0):
            return True
        res |= in_degree[root] != out_degree[root]
        return res

    for i in range(n_nodes):
        if state[i] == 0:
            if not dfs(i):
                return 'NO'

    return 'YES'


def main():
    res = solve()
    print(res)


if __name__ == '__main__':
    main()

```