Problem: Consider placing N flags on a line. Flags are numbered through 1 to N.

Flag i can be placed on the coordinate X_i or Y_i. For any two different flags, the distance between them should be at least D.

Decide whether it is possible to place all N flags. If it is possible, print such a configulation.

Constraints

* 1 \leq N \leq 1000
* 0 \leq D \leq 10^9
* 0 \leq X_i < Y_i \leq 10^9
* All values in Input are integer.

Input

Input is given from Standard Input in the following format:


N D
X_1 Y_1
X_2 Y_2
\vdots
X_N Y_N


Output

Print `No` if it is impossible to place N flags.

If it is possible, print `Yes` first. After that, print N lines. i-th line of them should contain the coodinate of flag i.

Examples

Input

3 2
1 4
2 5
0 6


Output

Yes
4
2
0


Input

3 3
1 4
2 5
0 6


Output

No

Solution (in JAVA):

Solution:
public class Main {
    public static void main(String[] args) throws Exception {
        var sc = new FastScanner();
        var pw = new FastPrintStream();
        solve(sc, pw);
        sc.close();
        pw.flush();
        pw.close();
    }

    public static void solve(FastScanner sc, FastPrintStream pw) {
        int n = sc.nextInt();
        int d = sc.nextInt();
        var x = new int[n];
        var y = new int[n];
        for (int i = 0; i < n; i++) {
            x[i] = sc.nextInt();
            y[i] = sc.nextInt();
        }
        var twosat = new TwoSAT(n);
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                int d00 = Math.abs(x[i] - x[j]);
                int d01 = Math.abs(x[i] - y[j]);
                int d10 = Math.abs(y[i] - x[j]);
                int d11 = Math.abs(y[i] - y[j]);
                if (d00 < d) twosat.addClause(i, true , j, true );
                if (d01 < d) twosat.addClause(i, true , j, false);
                if (d10 < d) twosat.addClause(i, false, j, true );
                if (d11 < d) twosat.addClause(i, false, j, false);
            }
        }
        boolean exists = twosat.satisfiable();
        if (!exists) {
            pw.println("No");
            return;
        }
        pw.println("Yes");
        var bitset = twosat.answer();
        for (int i = 0; i < n; i++) {
            pw.println(bitset.get(i) ? y[i] : x[i]);
        }
    }
}

class TwoSAT {
    private final int n;
    private final InternalSCC scc;
    private final java.util.BitSet answer;

    private boolean hasCalledSatisfiable = false;
    private boolean existsAnswer = false;

    public TwoSAT(int n) {
        this.n = n;
        this.scc = new InternalSCC(2 * n);
        this.answer = new java.util.BitSet(n);
    }

    public void addClause(int x, boolean f, int y, boolean g) {
        scc.addEdge(x << 1 | (f ? 0 : 1), y << 1 | (g ? 1 : 0));
        scc.addEdge(y << 1 | (g ? 0 : 1), x << 1 | (f ? 1 : 0));
    }

    public void addImplication(int x, boolean f, int y, boolean g) {
        addClause(x, !f, y, g);
    }

    public void addNand(int x, boolean f, int y, boolean g) {
        addClause(x, !f, y, !g);
    }

    public boolean satisfiable() {
        hasCalledSatisfiable = true;
        int[] ids = scc.ids();
        for (int i = 0; i < n; i++) {
            if (ids[i << 1 | 0] == ids[i << 1 | 1]) return existsAnswer = false;
            answer.set(i, ids[i << 1 | 0] < ids[i << 1 | 1]);
        }
        return existsAnswer = true;
    }

    public java.util.BitSet answer() {
        if (!hasCalledSatisfiable) {
            throw new UnsupportedOperationException(
                "Call TwoSAT#satisfiable at least once before TwoSAT#answer."
            );
        }
        if (existsAnswer) return answer;
        return null;
    }

    private static final class EdgeList {
        long[] a;
        int ptr = 0;
        EdgeList(int cap) {a = new long[cap];}
        void add(int upper, int lower) {
            if (ptr == a.length) grow();
            a[ptr++] = (long) upper << 32 | lower;
        }
        void grow() {
            long[] b = new long[a.length << 1];
            System.arraycopy(a, 0, b, 0, a.length);
            a = b;
        }
    }

    private static final class InternalSCC {
        final int n;
        int m;
        final EdgeList unorderedEdges;
        final int[] start;
        InternalSCC(int n) {
            this.n = n;
            this.unorderedEdges = new EdgeList(n);
            this.start = new int[n + 1];
        }
        void addEdge(int from, int to) {
            unorderedEdges.add(from, to);
            start[from + 1]++;
            this.m++;
        }
        static final long mask = 0xffff_ffffl;
        int[] ids() {
            for (int i = 1; i <= n; i++) {
                start[i] += start[i - 1];
            }
            int[] orderedEdges = new int[m];
            int[] count = new int[n + 1];
            System.arraycopy(start, 0, count, 0, n + 1);
            for (int i = 0; i < m; i++) {
                long e = unorderedEdges.a[i];
                orderedEdges[count[(int) (e >>> 32)]++] = (int) (e & mask);
            }
            int nowOrd = 0;
            int groupNum = 0;
            int k = 0;
            int[] par = new int[n];
            int[] vis = new int[n];
            int[] low = new int[n];
            int[] ord = new int[n];
            java.util.Arrays.fill(ord, -1);
            int[] ids = new int[n];
            long[] stack = new long[n];
            int ptr = 0;
            
            for (int i = 0; i < n; i++) {
                if (ord[i] >= 0) continue;
                par[i] = -1;
                stack[ptr++] = i;
                while (ptr > 0) {
                    long p = stack[--ptr];
                    int u = (int) (p & mask);
                    int j = (int) (p >>> 32);
                    if (j == 0) {
                        low[u] = ord[u] = nowOrd++;
                        vis[k++] = u;
                    }
                    if (start[u] + j < count[u]) {
                        int to = orderedEdges[start[u] + j];
                        stack[ptr++] += 1l << 32;
                        if (ord[to] == -1) {
                            stack[ptr++] = to;
                            par[to] = u;
                        } else {
                            low[u] = Math.min(low[u], ord[to]);
                        }
                    } else {
                        while (j --> 0) {
                            int to = orderedEdges[start[u] + j];
                            if (par[to] == u) low[u] = Math.min(low[u], low[to]);
                        }
                        if (low[u] == ord[u]) {
                            while (true) {
                                int v = vis[--k];
                                ord[v] = n;
                                ids[v] = groupNum;
                                if (v == u) break;
                            }
                            groupNum++;
                        }
                    }
                }
            }
            for (int i = 0; i < n; i++) {
                ids[i] = groupNum - 1 - ids[i];
            }
            return ids;
        }
    }
}

class FastPrintStream implements AutoCloseable {
    private static final int BUF_SIZE = 1 << 15;
    private final byte[] buf = new byte[BUF_SIZE];
    private int ptr = 0;
    private final java.lang.reflect.Field strField;
    private final java.nio.charset.CharsetEncoder encoder;

    private java.io.OutputStream out;

    public FastPrintStream(java.io.OutputStream out) {
        this.out = out;
        java.lang.reflect.Field f;
        try {
            f = java.lang.String.class.getDeclaredField("value");
            f.setAccessible(true);
        } catch (NoSuchFieldException | SecurityException e) {
            f = null;
        }
        this.strField = f;
        this.encoder = java.nio.charset.StandardCharsets.US_ASCII.newEncoder();
    }

    public FastPrintStream(java.io.File file) throws java.io.IOException {
        this(new java.io.FileOutputStream(file));
    }

    public FastPrintStream(java.lang.String filename) throws java.io.IOException {
        this(new java.io.File(filename));
    }

    public FastPrintStream() {
        this(System.out);
        try {
            java.lang.reflect.Field f = java.io.PrintStream.class.getDeclaredField("autoFlush");
            f.setAccessible(true);
            f.set(System.out, false);
        } catch (IllegalAccessException | IllegalArgumentException | NoSuchFieldException e) {
            // ignore
        }
    }

    public FastPrintStream println() {
        if (ptr == BUF_SIZE) internalFlush();
        buf[ptr++] = (byte) '\n';
        return this;
    }

    public FastPrintStream println(java.lang.Object o) {
        return print(o).println();
    }

    public FastPrintStream println(java.lang.String s) {
        return print(s).println();
    }

    public FastPrintStream println(char[] s) {
        return print(s).println();
    }

    public FastPrintStream println(char c) {
        return print(c).println();
    }

    public FastPrintStream println(int x) {
        return print(x).println();
    }

    public FastPrintStream println(long x) {
        return print(x).println();
    }

    public FastPrintStream println(double d, int precision) {
        return print(d, precision).println();
    }

    private FastPrintStream print(byte[] bytes) {
        int n = bytes.length;
        if (ptr + n > BUF_SIZE) {
            internalFlush();
            try {
                out.write(bytes);
            } catch (java.io.IOException e) {
                throw new RuntimeException();
            }
        } else {
            System.arraycopy(bytes, 0, buf, ptr, n);
            ptr += n;
        }
        return this;
    }

    public FastPrintStream print(java.lang.Object o) {
        return print(o.toString());
    }

    public FastPrintStream print(java.lang.String s) {
        if (strField == null) {
            return print(s.getBytes());
        } else {
            try {
                return print((byte[]) strField.get(s));
            } catch (IllegalAccessException e) {
                return print(s.getBytes());
            }
        }
    }

    public FastPrintStream print(char[] s) {
        try {
            return print(encoder.encode(java.nio.CharBuffer.wrap(s)).array());
        } catch (java.nio.charset.CharacterCodingException e) {
            byte[] bytes = new byte[s.length];
            for (int i = 0; i < s.length; i++) {
                bytes[i] = (byte) s[i];
            }
            return print(bytes);
        }
    }

    public FastPrintStream print(char c) {
        if (ptr == BUF_SIZE) internalFlush();
        buf[ptr++] = (byte) c;
        return this;
    }

    public FastPrintStream print(int x) {
        if (x == 0) {
            if (ptr == BUF_SIZE) internalFlush();
            buf[ptr++] = '0';
            return this;
        }
        int d = len(x);
        if (ptr + d > BUF_SIZE) internalFlush();
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr += d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        return this;
    }

    public FastPrintStream print(long x) {
        if (x == 0) {
            if (ptr == BUF_SIZE) internalFlush();
            buf[ptr++] = '0';
            return this;
        }
        int d = len(x);
        if (ptr + d > BUF_SIZE) internalFlush();
        if (x < 0) {
            buf[ptr++] = '-';
            x = -x;
            d--;
        }
        int j = ptr += d; 
        while (x > 0) {
            buf[--j] = (byte) ('0' + (x % 10));
            x /= 10;
        }
        return this;
    }

    public FastPrintStream print(double d, int precision) {
        if (d < 0) {
            print('-');
            d = -d;
        }
        d += Math.pow(10, -d) / 2;
        print((long) d).print('.');
        d -= (long) d;
        for(int i = 0; i < precision; i++){
            d *= 10;
            print((int) d);
            d -= (int) d;
        }
        return this;
    }

    private void internalFlush() {
        try {
            out.write(buf, 0, ptr);
            ptr = 0;
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void flush() {
        try {
            out.write(buf, 0, ptr);
            out.flush();
            ptr = 0;
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    public void close() {
        try {
            out.close();
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }

    private static int len(int x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        int p = -10;
        for (int i = 1; i < 10; i++, p *= 10) if (x > p) return i + d;
        return 10 + d;
    }

    private static int len(long x) {
        int d = 1;
        if (x >= 0) {d = 0; x = -x;}
        long p = -10;
        for (int i = 1; i < 19; i++, p *= 10) if (x > p) return i + d;
        return 19 + d;
    }
}

class FastScanner implements AutoCloseable {
    private final java.io.InputStream in;
    private final byte[] buf = new byte[2048];
    private int ptr = 0;
    private int buflen = 0;

    public FastScanner(java.io.InputStream in) {
        this.in = in;
    }

    public FastScanner() {
        this(System.in);
    }

    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {
            buflen = in.read(buf);
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
        return buflen > 0;
    }

    private int readByte() {
        return hasNextByte() ? buf[ptr++] : -1;
    }

    public boolean hasNext() {
        while (hasNextByte() && !(32 < buf[ptr] && buf[ptr] < 127)) ptr++;
        return hasNextByte();
    }

    private StringBuilder nextSequence() {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        for (int b = readByte(); 32 < b && b < 127; b = readByte()) {
            sb.appendCodePoint(b);
        }
        return sb;
    }

    public String next() {
        return nextSequence().toString();
    }

    public String next(int len) {
        return new String(nextChars(len));
    }

    public char nextChar() {
        if (!hasNextByte()) throw new java.util.NoSuchElementException();
        return (char) readByte();
    }

    public char[] nextChars() {
        StringBuilder sb = nextSequence();
        int l = sb.length();
        char[] dst = new char[l];
        sb.getChars(0, l, dst, 0);
        return dst;
    }
    public char[] nextChars(int len) {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        char[] s = new char[len];
        int i = 0;
        int b = readByte();
        while (32 < b && b < 127 && i < len) {
            s[i++] = (char) b; b = readByte();
        }
        if (i != len) {
            throw new java.util.NoSuchElementException(
                String.format("Next token has smaller length than expected.", len)
            );
        }
        return s;
    }
    public long nextLong() {
        if (!hasNext()) throw new java.util.NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) throw new NumberFormatException();
        while (true) {
            if ('0' <= b && b <= '9') {
                n = n * 10 + b - '0';
            } else if (b == -1 || !(32 < b && b < 127)) {
                return minus ? -n : n;
            } else throw new NumberFormatException();
            b = readByte();
        }
    }
    public int nextInt() {
        return Math.toIntExact(nextLong());
    }
    public double nextDouble() {
        return Double.parseDouble(next());
    }
    public void close() {
        try {
            in.close();
        } catch (java.io.IOException e) {
            throw new RuntimeException(e);
        }
    }
}