Problem: Niwango-kun, an employee of Dwango Co., Ltd., likes Niconico TV-chan, so he collected a lot of soft toys of her and spread them on the floor.

Niwango-kun has N black rare soft toys of Niconico TV-chan and they are spread together with ordinary ones. He wanted these black rare soft toys to be close together, so he decided to rearrange them.

In an infinitely large two-dimensional plane, every lattice point has a soft toy on it. The coordinates (x_i,y_i) of N black rare soft toys are given. All soft toys are considered to be points (without a length, area, or volume).

He may perform the following operation arbitrarily many times:

* Put an axis-aligned square with side length D, rotate the square by 90 degrees with four soft toys on the four corners of the square. More specifically, if the left bottom corner's coordinate is (x, y), rotate four points (x,y) \rightarrow (x+D,y) \rightarrow (x+D,y+D) \rightarrow (x,y+D) \rightarrow (x,y) in this order. Each of the four corners of the square must be on a lattice point.



Let's define the scatteredness of an arrangement by the minimum side length of an axis-aligned square enclosing all black rare soft toys. Black rare soft toys on the edges or the vertices of a square are considered to be enclosed by the square.

Find the minimum scatteredness after he performs arbitrarily many operations.

Constraints

* 2 \leq N \leq 10^5
* 1 \leq D \leq 1000
* 0 \leq x_i, y_i \leq 10^9
* Given coordinates are pairwise distinct
* All numbers given in input are integers

Input

Input is given from Standard Input in the following format:


N D
x_1 y_1
:
x_N y_N


Output

Print the answer.

Examples

Input

3 1
0 0
1 0
2 0


Output

1


Input

19 2
1 3
2 3
0 1
1 1
2 1
3 1
4 4
5 4
6 4
7 4
8 4
8 3
8 2
8 1
8 0
7 0
6 0
5 0
4 0


Output

4


Input

8 3
0 0
0 3
3 0
3 3
2 2
2 5
5 2
5 5


Output

4

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            DSquareRotation solver = new DSquareRotation();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class DSquareRotation {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int d = in.readInt();
            int d2 = d * 2;
            int[][] mat = new int[d2][d2];
            int[][][] sum = new int[3][d2][d2];
            for (int i = 0; i < n; i++) {
                int x = DigitUtils.mod(in.readInt(), d);
                int y = DigitUtils.mod(in.readInt(), d);
                mat[x][y]++;
            }
            for (int i = 0; i < d2; i++) {
                for (int j = 0; j < d2; j++) {
                    mat[i][j] = mat[i % d][j % d];
                }
            }

            IntBinarySearch ibs = new IntBinarySearch() {

                public boolean check(int mid) {
                    //0
                    int a = mid / d;
                    int b = mid % d;
                    long[] limits = new long[]{(long) a * a, (long) a * (a + 1), (long) (a + 1) * (a + 1)};
                    for (int t = 0; t < 3; t++) {
                        for (int i = 0; i < d2; i++) {
                            for (int j = 0; j < d2; j++) {
                                sum[t][i][j] = mat[i][j] > limits[t] ? 1 : 0;
                            }
                        }
                    }
                    for (int t = 0; t < 3; t++) {
                        for (int i = 0; i < d2; i++) {
                            for (int j = 0; j < d2; j++) {
                                if (j > 0) {
                                    sum[t][i][j] += sum[t][i][j - 1];
                                }
                            }
                        }
                    }
                    for (int t = 0; t < 3; t++) {
                        for (int i = 0; i < d2; i++) {
                            for (int j = 0; j < d2; j++) {
                                if (i > 0) {
                                    sum[t][i][j] += sum[t][i - 1][j];
                                }
                            }
                        }
                    }

                    for (int i = 0; i < d; i++) {
                        for (int j = 0; j < d; j++) {
                            int total = interval(sum[2], i, j, i + b - 1, j + b - 1)
                                    + interval(sum[1], i + b, j, i + d - 1, j + b - 1)
                                    + interval(sum[1], i, j + b, i + b - 1, j + d - 1)
                                    + interval(sum[0], i + b, j + b, i + d - 1, j + d - 1);
                            if (total == 0) {
                                return true;
                            }
                        }
                    }
                    return false;
                }
            };

            int ans = ibs.binarySearch(0, (int) 1e9) - 1;
            out.println(ans);
        }

        public int interval(int[][] sum, int x1, int y1, int x2, int y2) {
            if (x1 > x2 || y1 > y2) {
                return 0;
            }
            int ans = sum[x2][y2];
            if (x1 > 0) {
                ans -= sum[x1 - 1][y2];
            }
            if (y1 > 0) {
                ans -= sum[x2][y1 - 1];
            }
            if (x1 > 0 && y1 > 0) {
                ans += sum[x1 - 1][y1 - 1];
            }
            return ans;
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 20];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class DigitUtils {
        private DigitUtils() {
        }

        public static int mod(int x, int mod) {
            x %= mod;
            if (x < 0) {
                x += mod;
            }
            return x;
        }

    }

    static abstract class IntBinarySearch {
        public abstract boolean check(int mid);

        public int binarySearch(int l, int r) {
            if (l > r) {
                throw new IllegalArgumentException();
            }
            while (l < r) {
                int mid = (l + r) >>> 1;
                if (check(mid)) {
                    r = mid;
                } else {
                    l = mid + 1;
                }
            }
            return l;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(int c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }
}