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
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int h = in.nextInt();
            int[][] g = new int[2 * h + 1][2 * h + 1];
            for (int i = 0; i < n; ++i) {
                int a = in.nextInt();
                int b = in.nextInt();
                int c = in.nextInt();
                int d = in.nextInt();
                int left;
                if (c == 0) {
                    left = h - a;
                } else {
                    left = h + c;
                }
                int right;
                if (d == 0) {
                    right = h + b;
                } else {
                    right = h - d;
                }
                ++g[left][right];
            }
            int[] outdeg = new int[g.length];
            int[] indeg = new int[g.length];
            for (int i = 0; i < g.length; ++i) {
                for (int j = 0; j < g.length; ++j) {
                    outdeg[i] += g[i][j];
                    indeg[j] += g[i][j];
                }
            }
            for (int i = 0; i < h; ++i) {
                int delta = outdeg[i] - indeg[i];
                if (delta < 0) {
                    out.println("NO");
                    return;
                }
                g[0][i] += delta;
            }
            for (int i = h + 1; i < g.length; ++i) {
                int delta = indeg[i] - outdeg[i];
                if (delta < 0) {
                    out.println("NO");
                    return;
                }
                g[i][0] += delta;
            }
            boolean[] mark = new boolean[g.length];
            dfs(0, g, mark);
            for (int i = 0; i < g.length; ++i)
                if (!mark[i] && outdeg[i] + indeg[i] > 0) {
                    out.println("NO");
                    return;
                }
            out.println("YES");
        }

        private void dfs(int i, int[][] g, boolean[] mark) {
            if (mark[i]) return;
            mark[i] = true;
            for (int j = 0; j < g.length; ++j)
                if (g[i][j] != 0 || g[j][i] != 0) {
                    dfs(j, g, mark);
                }
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

