Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

3 2
1 4
2 5
0 6

Sample Output 1

Yes
4
2
0

Sample Input 2

3 3
1 4
2 5
0 6

Sample Output 2

No

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Threading;
using System.Runtime.CompilerServices;
using System.Text;
using System.Diagnostics;
using System.Numerics;
using static System.Console;
using static System.Convert;
using static System.Math;
using static Template;
using SC = FastScanner;

public partial class Solver
{
    public void Solve()
    {
        int N = sc.Int, D = sc.Int;
        var ts = new TwoSat(N);
        int[] X=new int[N], Y=new int[N];
        for(int i = 0; i < N; i++)
        {
            X[i] = sc.Int;Y[i] = sc.Int;
            for(int j = 0; j < i; j++)
            {
                if (Abs(X[i] - X[j]) < D)
                {
                    ts.AddClosure(i, false, j, false);
                }
                if (Abs(Y[i] - Y[j]) < D)
                {
                    ts.AddClosure(i, true, j, true);
                }
                if (Abs(X[i] - Y[j]) < D)
                {
                    ts.AddClosure(i, false, j, true);
                }
                if (Abs(Y[i] - X[j]) < D)
                {
                    ts.AddClosure(i, true, j, false);
                }
            }
        }
        if (!ts.Execute()) Fail("No");
        Console.WriteLine("Yes");
        for (int i = 0; i < ts.Answer.Length; i++)
            if (ts.Answer[i]) Console.WriteLine(X[i]);
            else Console.WriteLine(Y[i]);

    }
}
class TwoSat
{
    StronglyConnectedComponents scc;
    public bool[] Answer { get; private set; }
    public TwoSat(int N)
    {
        scc = new StronglyConnectedComponents(N << 1);
        Answer = new bool[N];
    }
    //(x_i=f)V(x_j=g) <-> !(x_i=f)->(x_j=g) <-> !(x_j=g)->(x_i=f)の追加
    public void AddClosure(int i, bool f, int j, bool g)
    {
        scc.AddEdge((i << 1) | (f ? 0 : 1), (j << 1) | (g ? 1 : 0));
        scc.AddEdge((j << 1) | (g ? 0 : 1), (i << 1) | (f ? 1 : 0));
    }
    public bool Execute()
    {
        scc.Execute();
        var gp = scc.Group;
        var len = gp.Length >> 1;
        for (int i = 0; i < len; i++)
        {
            if (gp[i << 1] == gp[(i << 1) | 1]) return false;
            Answer[i] = gp[i<<1] < gp[(i<<1)|1];//DAG
        }
        return true;
    }
}

public class StronglyConnectedComponents
{
    int size;
    List<Edge> edges;
    private int[][] scc;
    public int Count { get; private set; }
    public int[] Group { get; private set; }
    public int[] GroupAt(int k) => scc[k];
    public StronglyConnectedComponents(int count)
    {
        size = count;
        edges = new List<Edge>();
    }
    public void AddEdge(int from, int to)
    {
        edges.Add(new Edge(from, to));
    }
    /// <summary>
    /// O(V+E)
    /// </summary>
    /// <returns>scc[i]:i番目の強連結成分の頂点</returns>
    public int[][] Execute()
    {
        //e.fromでe.toをソート
        var start = new int[size + 1];
        var toList = new int[edges.Count];
        foreach (var e in edges) start[e.from + 1]++;
        for (int i = 0; i < start.Length - 1; i++) start[i + 1] += start[i];
        var count = start.ToArray();
        foreach (var e in edges) toList[count[e.from]++] = e.to;
        //lowlink
        int nowOrd = 0;
        int[] low = new int[size], ord = new int[size];
        Group = new int[size];
        var stack = new Stack<int>(size);
        for (int i = 0; i < ord.Length; i++) ord[i] = -1;
        Action<int> dfs = null;
        dfs = v =>
        {
            low[v] = ord[v] = nowOrd++;
            stack.Push(v);
            for (int i = start[v]; i < start[v + 1]; i++)
            {
                var to = toList[i];
                if (ord[to] == -1)
                {
                    dfs(to);
                    low[v] = Min(low[v], low[to]);
                }
                else low[v] = Min(low[v], ord[to]);
            }
            if (low[v] == ord[v])
            {
                while (true)
                {
                    var u = stack.Pop();
                    ord[u] = size;
                    Group[u] = Count;
                    if (u == v) break;
                }
                Count++;
            }
        };
        for (int i = 0; i < ord.Length; i++)
        {
            if (ord[i] == -1) dfs(i);
        }
        for (int i = 0; i < Group.Length; i++)
        {
            Group[i] = Count - 1 - Group[i];
            count[i] = 0;
        }
        scc = new int[Count][];
        foreach (var g in Group) count[g]++;
        for (int i = 0; i < scc.Length; i++) scc[i] = new int[count[i]];
        for (int i = 0; i < Group.Length; i++) scc[Group[i]][--count[Group[i]]] = i;
        return scc;
    }
    struct Edge { public int from, to; public Edge(int f, int t) { from = f; to = t; } }
}

public class FastScanner
{
    //0x0a:LF 0x20:SPC 0x2d:- 0x30 ~ 0x39: 0 ~ 9
    static System.IO.Stream str = System.Console.OpenStandardInput();
    const int size = 1 << 10;
    static byte[] buffer = new byte[size];
    static int ptr;
    static int len;
    public int Int
    {
        get
        {
            var c = Read();
            while (c < 0x21)
            {
                c = Read();
            }
            var n = false;
            if (c == '-')
            {
                n = true;
                c = Read();
            }
            var ret = 0;
            while (c >= 0x30)
            {
                ret = ret * 10 + (c & 15);
                c = Read();
            }
            return n ? -ret : ret;
        }
    }
    public long Long
    {
        get
        {
            var c = Read();
            while (c < 0x21)
            {
                c = Read();
            }
            var n = false;
            if (c == '-')
            {
                n = true;
                c = Read();
            }
            var ret = 0L;
            while (c >= 0x30)
            {
                ret = ret * 10 + (c & 15);
                c = Read();
            }
            return n ? -ret : ret;
        }
    }
    byte Read()
    {
        if (ptr == len)
        {
            len = str.Read(buffer, 0, size);
            if (len == 0) return 0;
            ptr = 0;
        }
        return buffer[ptr++];
    }
}
#region Template
public partial class Solver
{
    public SC sc = new SC();
    static void Main(string[] args)
    {
        Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
        var sol = new Solver();
        int testcase = 1;
        //testcase = sol.sc.Int;
        //var th = new Thread(sol.Solve, 1 << 26);th.Start();th.Join();
        while (testcase-- > 0)
            sol.Solve();
        Console.Out.Flush();
    }
}
public static class Template
{
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmin<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) > 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static bool chmax<T>(ref T a, T b) where T : IComparable<T> { if (a.CompareTo(b) < 0) { a = b; return true; } return false; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(ref T a, ref T b) { var t = b; b = a; a = t; }
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public static void swap<T>(this IList<T> A, int i, int j) { var t = A[i]; A[i] = A[j]; A[j] = t; }
    public static T[] Create<T>(int n, Func<T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(); return rt; }
    public static T[] Create<T>(int n, Func<int, T> f) { var rt = new T[n]; for (var i = 0; i < rt.Length; ++i) rt[i] = f(i); return rt; }
    public static void Out<T>(this IList<T> A, out T a) => a = A[0];
    public static void Out<T>(this IList<T> A, out T a, out T b) { a = A[0]; b = A[1]; }
    public static void Out<T>(this IList<T> A, out T a, out T b, out T c) { A.Out(out a, out b); c = A[2]; }
    public static void Out<T>(this IList<T> A, out T a, out T b, out T c, out T d) { A.Out(out a, out b, out c); d = A[3]; }
    public static string Concat<T>(this IEnumerable<T> A, string sp) => string.Join(sp, A);
    public static char ToChar(this int s, char begin = '0') => (char)(s + begin);
    public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> A) => A.OrderBy(v => Guid.NewGuid());
    public static int CompareTo<T>(this T[] A, T[] B, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; for (var i = 0; i < Min(A.Length, B.Length); i++) { int c = cmp(A[i], B[i]); if (c > 0) return 1; else if (c < 0) return -1; } if (A.Length == B.Length) return 0; if (A.Length > B.Length) return 1; else return -1; }
    public static string ToStr<T>(this T[][] A) => A.Select(a => a.Concat(" ")).Concat("\n");
    public static int ArgMax<T>(this IList<T> A, Comparison<T> cmp = null) { cmp = cmp ?? Comparer<T>.Default.Compare; T max = A[0]; int rt = 0; for (int i = 1; i < A.Count; i++) if (cmp(max, A[i]) < 0) { max = A[i]; rt = i; } return rt; }
    public static T PopBack<T>(this List<T> A) { var v = A[A.Count - 1]; A.RemoveAt(A.Count - 1); return v; }
    public static void Fail<T>(T s) { Console.WriteLine(s); Console.Out.Close(); Environment.Exit(0); }
}
public class Scanner
{
    public string Str => Console.ReadLine().Trim();
    public int Int => int.Parse(Str);
    public long Long => long.Parse(Str);
    public double Double => double.Parse(Str);
    public int[] ArrInt => Str.Split(' ').Select(int.Parse).ToArray();
    public long[] ArrLong => Str.Split(' ').Select(long.Parse).ToArray();
    public char[][] Grid(int n) => Create(n, () => Str.ToCharArray());
    public int[] ArrInt1D(int n) => Create(n, () => Int);
    public long[] ArrLong1D(int n) => Create(n, () => Long);
    public int[][] ArrInt2D(int n) => Create(n, () => ArrInt);
    public long[][] ArrLong2D(int n) => Create(n, () => ArrLong);
    private Queue<string> q = new Queue<string>();
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    public T Next<T>() { if (q.Count == 0) foreach (var item in Str.Split(' ')) q.Enqueue(item); return (T)Convert.ChangeType(q.Dequeue(), typeof(T)); }
    public void Make<T1>(out T1 v1) => v1 = Next<T1>();
    public void Make<T1, T2>(out T1 v1, out T2 v2) { v1 = Next<T1>(); v2 = Next<T2>(); }
    public void Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3) { Make(out v1, out v2); v3 = Next<T3>(); }
    public void Make<T1, T2, T3, T4>(out T1 v1, out T2 v2, out T3 v3, out T4 v4) { Make(out v1, out v2, out v3); v4 = Next<T4>(); }
    public void Make<T1, T2, T3, T4, T5>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5) { Make(out v1, out v2, out v3, out v4); v5 = Next<T5>(); }
    public void Make<T1, T2, T3, T4, T5, T6>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6) { Make(out v1, out v2, out v3, out v4, out v5); v6 = Next<T6>(); }
    public void Make<T1, T2, T3, T4, T5, T6, T7>(out T1 v1, out T2 v2, out T3 v3, out T4 v4, out T5 v5, out T6 v6, out T7 v7) { Make(out v1, out v2, out v3, out v4, out v5, out v6); v7 = Next<T7>(); }
    public (T1, T2) Make<T1, T2>() { Make(out T1 v1, out T2 v2); return (v1, v2); }
    public (T1, T2, T3) Make<T1, T2, T3>() { Make(out T1 v1, out T2 v2, out T3 v3); return (v1, v2, v3); }
    public (T1, T2, T3, T4) Make<T1, T2, T3, T4>() { Make(out T1 v1, out T2 v2, out T3 v3, out T4 v4); return (v1, v2, v3, v4); }
}

#endregion