Problem:
Score : 900 points

Problem Statement

You are in charge of controlling a dam. The dam can store at most L liters of water. Initially, the dam is empty. Some amount of water flows into the dam every morning, and any amount of water may be discharged every night, but this amount needs to be set so that no water overflows the dam the next morning.

It is known that v_i liters of water at t_i degrees Celsius will flow into the dam on the morning of the i-th day.
You are wondering about the maximum possible temperature of water in the dam at noon of each day, under the condition that there needs to be exactly L liters of water in the dam at that time. For each i, find the maximum possible temperature of water in the dam at noon of the i-th day. Here, consider each maximization separately, that is, the amount of water discharged for the maximization of the temperature on the i-th day, may be different from the amount of water discharged for the maximization of the temperature on the j-th day (j≠i).

Also, assume that the temperature of water is not affected by anything but new water that flows into the dam. That is, when V_1 liters of water at T_1 degrees Celsius and V_2 liters of water at T_2 degrees Celsius are mixed together, they will become V_1+V_2 liters of water at \frac{T_1*V_1+T_2*V_2}{V_1+V_2} degrees Celsius, and the volume and temperature of water are not affected by any other factors.

Constraints

1≤ N ≤ 5*10^5

1≤ L ≤ 10^9

0≤ t_i ≤ 10^9(1≤i≤N)

1≤ v_i ≤ L(1≤i≤N)

v_1 = L

L, each t_i and v_i are integers.

Input

Input is given from Standard Input in the following format:

N L
t_1 v_1
t_2 v_2
:
t_N v_N

Output

Print N lines. The i-th line should contain the maximum temperature such that it is possible to store L liters of water at that temperature in the dam at noon of the i-th day.

Each of these values is accepted if the absolute or relative error is at most 10^{-6}.

Sample Input 1

3 10
10 10
20 5
4 3

Sample Output 1

10.0000000
15.0000000
13.2000000

On the first day, the temperature of water in the dam is always 10 degrees: the temperature of the only water that flows into the dam on the first day.

10 liters of water at 15 degrees of Celsius can be stored on the second day, by discharging 5 liters of water on the night of the first day, and mix the remaining water with the water that flows into the dam on the second day.

10 liters of water at 13.2 degrees of Celsius can be stored on the third day, by discharging 8 liters of water on the night of the first day, and mix the remaining water with the water that flows into the dam on the second and third days.

Sample Input 2

4 15
0 15
2 5
3 6
4 4

Sample Output 2

0.0000000
0.6666667
1.8666667
2.9333333

Sample Input 3

4 15
1000000000 15
9 5
8 6
7 4

Sample Output 3

1000000000.0000000
666666669.6666666
400000005.0000000
293333338.8666667

Although the temperature of water may exceed 100 degrees Celsius, we assume that water does not vaporize.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using SB = System.Text.StringBuilder;
//using System.Numerics;
using static System.Math;
namespace Program {
    public class Solver {
        Random rnd = new Random(0);
        public void Solve() {
            var n = ri;
            var L = rl;
            var deq = new Deque<X>();
            double sum = 0;
            for (int _ = 0; _ < n; _++)
            {
                var x = new X(ri, ri);
                sum += x.temp * x.vol;
                if (deq.Count == 0) { deq.PushBack(x); }
                else
                {
                    //水を捨てておく
                    {
                        var v = x.vol;
                        while (v > 0)
                        {
                            var p = deq.PopFront(); sum -= p.temp * p.vol;
                            var mi = Math.Min(v, p.vol);
                            p.vol -= mi; v -= mi;
                            if (p.vol > 0)
                            {
                                deq.PushFront(p); sum += p.temp * p.vol;
                            }
                        }
                    }
                    while (deq.Count > 0 && deq[deq.Count - 1].temp >= x.temp)
                    {
                        var p = deq.PopBack();
                        var nv = x.vol + p.vol;
                        x = new X((x.temp * x.vol + p.temp * p.vol) / nv, nv);
                    }
                    deq.PushBack(x);

                }
                Console.WriteLine("{0:0.000000000000}", 1.0 * sum / L);
            }
        }

        class X {
            public double temp, vol;
            public X(double T, double V) {
                this.temp = T; vol = V;
            }
        }
        const long INF = 5L << 60;
        static int[] dx = { -1, 0, 1, 0 };
        static int[] dy = { 0, 1, 0, -1 };
        int ri { get { return sc.Integer(); } }
        long rl { get { return sc.Long(); } }
        double rd { get { return sc.Double(); } }
        string rs { get { return sc.Scan(); } }
        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

        static T[] Enumerate<T>(int n, Func<int, T> f) {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f(i);
            return a;
        }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex {
    static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
        return string.Join(st, ie);
    }
    static public void Main() {
        Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Program.Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO {
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer: StreamWriter {
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }

    public class StreamScanner {
        public StreamScanner(Stream stream) { str = stream; }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }

        private byte read() {
            if (isEof) return 0;
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }

        public char Char() {
            byte b = 0;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }
        public string Scan() {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine() {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}

#endregion


#region Deque<T>

public class Deque<T> {
    T[] buf;
    int offset, cnt;
    public int Count { get { return cnt; } }
    public Deque(int capacity) { buf = new T[capacity]; }
    public Deque() : this(8) { }
    public T this[int index] {
        get { return buf[getIndex(index)]; }
        set { buf[getIndex(index)] = value; }
    }
    int getIndex(int index) {
        if (index >= cnt) throw new ArgumentOutOfRangeException("out of range");
        var ret = index + offset;
        if (ret >= buf.Length)
            ret -= buf.Length;
        return ret;
    }
    public void PushFront(T item) {
        if (cnt == buf.Length) extend();
        if (--offset < 0) offset += buf.Length;
        buf[offset] = item;
        ++cnt;
    }
    public T PopFront() {
        if (cnt == 0) throw new ArgumentOutOfRangeException("collection is empty");
        --cnt;
        var ret = buf[offset++];
        if (offset >= buf.Length) offset -= buf.Length;
        return ret;
    }
    public void PushBack(T item) {
        if (cnt == buf.Length) extend();
        var id = cnt++ + offset;
        if (id >= buf.Length) id -= buf.Length;
        buf[id] = item;
    }
    public T PopBack() {
        if (cnt == 0)
            throw new ArgumentOutOfRangeException("collection is empty");
        var ret = buf[getIndex(cnt - 1)]; cnt--;
        return ret;
    }
    public void Insert(T item, int index) {
        if (index > cnt) throw new ArgumentOutOfRangeException();
        PushFront(item);
        for (int i = 0; i < index; i++)
            this[i] = this[i + 1];
        this[index] = item;
    }
    public T RemoveAt(int index) {
        if (index < 0 || index >= cnt) throw new ArgumentOutOfRangeException();
        var ret = this[index];
        for (int i = index; i > 0; i--)
            this[i] = this[i - 1];
        PopFront();
        return ret;
    }
    public bool Any() { return cnt > 0; }
    void extend() {
        T[] next = new T[buf.Length * 2];
        if (offset > buf.Length - cnt)
        {
            var len = buf.Length - offset;
            Array.Copy(buf, offset, next, 0, len);
            Array.Copy(buf, 0, next, len, cnt - len);
        }
        else Array.Copy(buf, offset, next, 0, cnt);
        buf = next;
        offset = 0;
    }
    public T[] Items {
        get {
            var a = new T[cnt];
            for (int i = 0; i < cnt; i++)
                a[i] = this[i];
            return a;
        }
    }
}

#endregion