Problem:
Score : 800 points

Problem Statement

Takahashi and Aoki will take N exams numbered 1 to N.
They have decided to compete in these exams.
The winner will be determined as follows:

For each exam i, Takahashi decides its importance c_i, which must be an integer between l_i and u_i (inclusive).

Let A be \sum_{i=1}^{N} c_i \times (Takahashi's score on Exam i), and B be \sum_{i=1}^{N} c_i \times (Aoki's score on Exam i). Takahashi wins if A \geq B, and Aoki wins if A < B.

Takahashi knows that Aoki will score b_i on Exam i, with his supernatural power.

Takahashi himself, on the other hand, will score 0 on all the exams without studying more. For each hour of study, he can increase his score on some exam by 1. (He can only study for an integer number of hours.)
However, he cannot score more than X on an exam, since the perfect score for all the exams is X.

Print the minimum number of study hours required for Takahashi to win.

Constraints

1 \leq N \leq 10^5

1 \leq X \leq 10^5

0 \leq b_i \leq X (1 \leq i \leq N)

1 \leq l_i \leq u_i \leq 10^5 (1 \leq i \leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N X
b_1 l_1 u_1
b_2 l_2 u_2
:
b_N l_N u_N

Output

Print the minimum number of study hours required for Takahashi to win.

Sample Input 1

2 100
85 2 3
60 1 1

Sample Output 1

115

One optimal strategy is as follows:

Choose c_1 = 3, c_2 = 1.

Study to score 100 on Exam 1 and 15 on Exam 2.

Then, A = 3 \times 100 + 1 \times 15 = 315, B = 3 \times 85 + 1 \times 60 = 315 and Takahashi will win.

Sample Input 2

2 100
85 2 3
60 10 10

Sample Output 2

77

Sample Input 3

1 100000
31415 2718 2818

Sample Output 3

31415

Sample Input 4

10 1000
451 4593 6263
324 310 6991
378 1431 7068
71 1757 9218
204 3676 4328
840 6221 9080
684 1545 8511
709 5467 8674
862 6504 9835
283 4965 9980

Sample Output 4

2540

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Collections.Generic;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using Debug = System.Diagnostics.Debug;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;

static class P
{
    static void Main()
    {
        var n = Read();
        var X = Read();
        //捨てるテストは重要度l、勉強するテストは重要度uとする
        //取っていきたい勉強を決める
        //勉強する勉強を決め打つと楽になる
        //勉強するテストは全てbより多く勉強することは確定?いいえ
        //まず、限界までテストは勉強する(最後除く)bが点と同じなので
        //b未満の場合、重要度はuよりはlの方が良いことが分かる
        //もし他の勉強でuがl以上のものがあった場合はそれを優先したい
        //捨てたときのペナ-(b*l)と取ったときのコスト((x-b)*u)の差が大きい方から取り、全ペナの合計ギリギリまで詰める
        //最後はどれで詰めるかは全探索で良い(lで負の状態ながらケチケチ詰めるケースもあれば、uで正に飛ばしてぶっ飛ばすケースもある)
        var b = new long[n];
        var l = new long[n];
        var u = new long[n];
        for (int i = 0; i < n; i++)
        {
            b[i] = Read();
            l[i] = Read();
            u[i] = Read();
        }
        var penaltySum = Enumerable.Range(0, n).Sum(i => b[i] * l[i]);
        var ordered = Enumerable.Range(0, n).OrderByDescending(i => (X - b[i]) * u[i] + b[i] * l[i]).ToArray();
        bool[] used = new bool[n];

        //最後にmaxまで取らないケースは確実にorderedのスコアよりは低くなるが、以上のスコアを持つために(何故ならばn*lなので)それが網羅されないことはない
        long res = 0;
        for (int i = 0; i < ordered.Length; i++)
        {
            //X点まで勉強したときの削減可能点差()
            var score = (X - b[ordered[i]]) * u[ordered[i]] + b[ordered[i]] * l[ordered[i]];
            if (penaltySum < score) break;
            used[ordered[i]] = true;
            penaltySum -= score;
            res += X;
        }
        long minTime = long.MaxValue;
        for (int i = 0; i < n; i++)
        {
            if (used[i]) continue;
            long time = 0;
            if (penaltySum <= b[i] * l[i])
            {
                time = (penaltySum + l[i] - 1) / l[i];
            }
            else
            {
                time = ((penaltySum - b[i] * l[i]) + u[i] - 1) / u[i] + b[i];
            }
            minTime = Min(minTime, time);
        }
        Console.WriteLine(res + minTime);
    }

    static readonly TextReader In = Console.In;
    [MethodImpl(MethodImplOptions.AggressiveInlining)]
    static int Read()
    {
        int res = 0;
        int next = In.Read();
        while (48 > next || next > 57) next = In.Read();
        while (48 <= next && next <= 57)
        {
            res = res * 10 + next - 48;
            next = In.Read();
        }
        return res;
    }

}