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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.NoSuchElementException;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {
	private static void solve() {
		int n = nei();
		int x = nei();
		long[][] blu = nls2(n, 3);
		long[][] ad = new long[n][2];// ad, idx
		long left = 0;
		for (int i = 0; i < n; i++) {
			long b = blu[i][0];
			long l = blu[i][1];
			long u = blu[i][2];
			ad[i][0] = b * l + (x - b) * u;
			ad[i][1] = i;
			left += b * l;
		}

		Arrays.sort(ad, (a, b) -> Long.signum(b[0] - a[0]));
		long ans = 0;
		for (int i = 0; i < n; i++) {
			long adi = ad[i][0];

//			System.out.println("left=" + left + ", ad[i]=" + adi);

			if (left < adi) {
//				System.out.println("overkill, check all");
				long minT = x;
				for (int j = i; j < n; j++) {
					int idx = (int) ad[j][1];

					long score = left;

					long b = blu[idx][0];
					long l = blu[idx][1];
					long u = blu[idx][2];

//					System.out.println(b + " " + l + " " + u);
					long num = (score + l - 1) / l;
//					System.out.println("left-1: " + score + " " + num);
					if (num <= b) {
						minT = min(minT, num);
						continue;
					}
					score -= l * b;
					num = b + (score + u - 1) / u;
//					System.out.println("left-2: " + score + " " + num);
					if (num <= x) {
						minT = min(minT, num);
						continue;
					}
					score -= (x - b) * u;
//					System.out.println("left-3: " + score);
					continue;
				}
//				System.out.println("min: " + minT);
				ans += minT;
				kil(ans);
			}
			left -= adi;
			ans += x;
		}
		kil(ans);
//
//		Arrays.sort(blu, (a, b) -> Long.signum(b[1] - a[1]));
//		long score = 0;
//		for (int i = 0; i < n; i++) {
//			score += blu[i][0] * blu[i][1];
//			System.out.println(blu[i][0] + " " + blu[i][1] + " " + blu[i][2]);
//		}
//		System.out.println();
//		long ans = 0;
//		for (int i = 0; i < n; i++) {
//			long b = blu[i][0];
//			long l = blu[i][1];
//			long u = blu[i][2];
//
//			System.out.println(b + " " + l + " " + u);
//			long num = (score + l - 1) / l;
//			System.out.println("left-1: " + score + " " + num);
//			if (num <= b) {
//				ans += num;
//				kil(ans);
//			}
//			score -= l * b;
//			ans += b;
//			System.out.println("left-2: " + score + " " + num);
//			num = (score + u - 1) / u;
//			if (b + num <= x) {
//				ans += num;
//				kil(ans);
//			}
//			score -= (x - b) * u;
//			ans += x - b;
//			System.out.println("left-3: " + score);
//		}
	}

	// returns (x, y, d) s.t. ax + by = d
	static long[] exgcd(long a, long b) {
		int sa = a < 0 ? -1 : 1;
		int sb = b < 0 ? -1 : 1;
		a *= sa;
		b *= sb;
		long x = 1;
		long y = 0;
		long z = 0;
		long w = 1;
		while (b > 0) {
			long q = a / b;
			long t = z;
			z = x - q * z;
			x = t;
			t = w;
			w = y - q * w;
			y = t;
			t = b;
			b = a - q * b;
			a = t;
		}
		return new long[] { x * sa, y * sb, a };
	}

	static int[] lis(int[] s) {
		int n = s.length;
		int[] dp = new int[n];
		int[] ids = new int[n];
		int[] pids = new int[n];
		dp[0] = s[0];
		int len = 1;
		int lidx = 0;
		for (int i = 1; i < n; i++) {
			int idx = bs(s[i], dp, 0, len);
			dp[idx] = s[i];
			ids[idx] = i;
			if (idx == len) {
				lidx = i;
				len++;
			}
			if (idx > 0)
				pids[i] = ids[idx - 1];
		}
		int[] lis = new int[len];
		lis[len - 1] = s[lidx];
		for (int i = len - 1; i >= 0; i--) {
			lis[i] = s[lidx];
			lidx = pids[lidx];
		}
		return lis;
	}

	static int bs(int a, int[] as, int from, int num) {
		int min = from;
		int max = from + num - 1;
		while (min < max) {
			int mid = min + max >> 1;
			if (as[mid] < a)
				min = mid + 1;
			else if (as[mid] > a)
				max = mid;
			else
				return mid;
		}
		return as[min] < a ? min + 1 : min;
	}

	static int gcd(int x, int y) {
		x = (x ^ x >> 31) - (x >> 31);
		y = (y ^ y >> 31) - (y >> 31);
		if (x < y) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		int z = x % y;
		if (z == 0)
			return y;
		return gcd(y, z);
	}

	static long gcd(long x, long y) {
		x = (x ^ x >> 63) - (x >> 63);
		y = (y ^ y >> 63) - (y >> 63);
		if (x < y) {
			x ^= y;
			y ^= x;
			x ^= y;
		}
		long z = x % y;
		if (z == 0)
			return y;
		return gcd(y, z);
	}

	static long modinv(long a, long mod) {
		return modpow(a, mod - 2, mod);
	}

	static long modpow(long a, long b, long mod) {
		if (b == 0)
			return 1;
		if ((b & 1) == 0) {
			long sqrt = modpow(a, b >> 1, mod);
			return sqrt * sqrt % mod;
		}
		return a * modpow(a, b - 1, mod) % mod;
	}

	static long fact(long n) {
		if (n <= 1)
			return 1;
		long res = 2;
		for (long i = 3; i <= n; i++) {
			res *= i;
		}
		return res;
	}

	static long modfact(long n, long mod) {
		if (n <= 1)
			return 1 % mod;
		long res = 2;
		for (long i = 3; i <= n; i++) {
			res *= i;
			res %= mod;
		}
		return res % mod;
	}

	// returns facts([0]) and invfacts([1])
	static long[][] enumfacts(int n, long mod) {
		int num = n + 10;
		long[][] res = new long[2][num];
		long[] facts = res[0];
		long[] invfacts = res[1];
		for (int i = 0; i < num; i++) {
			if (i <= 1) {
				facts[i] = 1;
				invfacts[i] = 1;
			} else {
				facts[i] = facts[i - 1] * i % mod;
				invfacts[i] = modinv(facts[i], mod);
			}
		}
		return res;
	}

	static long modcomb(long n, long m, long mod) {
		if (m > n)
			return 0;
		if (m > n - m) {
			m = n - m;
		}
		long numer = 1;
		for (int i = 0; i < m; i++) {
			numer = numer * (n - i) % mod;
		}
		long denom = modfact(m, mod);
		return numer * modinv(denom, mod) % mod;
	}

	static long modcomb(int n, int m, long[] facts, long[] invfacts, long mod) {
		if (m > n)
			return 0;
		long numer = facts[n];
		long denom = invfacts[m] * invfacts[n - m] % mod;
		return numer * denom % mod;
	}

	// res[i][0]: prime factor, res[i][1]: exponent
	static int[][] factorize(int n) {
		int[][] pfs = new int[32][2];
		int num = 0;
		for (int i = 2; i * i <= n; i++) {
			int count = 0;
			while (n % i == 0) {
				n /= i;
				count++;
			}
			if (count > 0) {
				pfs[num][0] = i;
				pfs[num][1] = count;
				num++;
			}
		}
		if (n > 1) {
			pfs[num][0] = n;
			pfs[num][1] = 1;
			num++;
		}
		int[][] res = new int[num][2];
		for (int i = 0; i < num; i++) {
			res[i][0] = pfs[i][0];
			res[i][1] = pfs[i][1];
		}
		return res;
	}

	static long lcm(long x, long y) {
		x = (x ^ x >> 63) - (x >> 63);
		y = (y ^ y >> 63) - (y >> 63);
		return x / gcd(x, y) * y;
	}

	static int abs(int x) {
		return x < 0 ? -x : x;
	}

	static long abs(long x) {
		return x < 0 ? -x : x;
	}

	static int min(int a, int b) {
		return a < b ? a : b;
	}

	static long min(long a, long b) {
		return a < b ? a : b;
	}

	static int max(int a, int b) {
		return a > b ? a : b;
	}

	static long max(long a, long b) {
		return a > b ? a : b;
	}

	static int clamp(int a, int min, int max) {
		return a < min ? min : a > max ? max : a;
	}

	static long clamp(long a, long min, long max) {
		return a < min ? min : a > max ? max : a;
	}

	static double clamp(double a, double min, double max) {
		return a < min ? min : a > max ? max : a;
	}

	static void out(String val) {
		IO.out(val);
	}

	static void out(Object val) {
		IO.out(String.valueOf(val));
	}

	static void out(int val) {
		IO.out(String.valueOf(val));
	}

	static void out(long val) {
		IO.out(String.valueOf(val));
	}

	static void out(char val) {
		IO.out(String.valueOf(val));
	}

	static void out(double val) {
		IO.out(Double.isFinite(val) ? BigDecimal.valueOf(val).toPlainString() : String.valueOf(val));
	}

	static void out(boolean val) {
		IO.out(val ? "true" : "false");
	}

	static void kil(String val) {
		IO.out(val);
		IO.flush();
		System.exit(0);
	}

	static void kil(Object val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(int val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(long val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(char val) {
		IO.out(String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(double val) {
		IO.out(Double.isFinite(val) ? BigDecimal.valueOf(val).toPlainString() : String.valueOf(val));
		IO.flush();
		System.exit(0);
	}

	static void kil(boolean val) {
		IO.out(val ? "true" : "false");
		IO.flush();
		System.exit(0);
	}

	static String nes() {
		return IO.next();
	}

	static int nei() {
		return IO.nextInt();
	}

	static long nel() {
		return IO.nextLong();
	}

	static double ned() {
		return IO.nextDouble();
	}

	static char nec() {
		return IO.nextChar();
	}

	static String[] nss(int n) {
		String[] as = new String[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.next();
		}
		return as;
	}

	static int[] nis(int n) {
		int[] as = new int[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextInt();
		}
		return as;
	}

	static long[] nls(int n) {
		long[] as = new long[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextLong();
		}
		return as;
	}

	static double[] nds(int n) {
		double[] as = new double[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextDouble();
		}
		return as;
	}

	static char[] ncs(int n) {
		char[] as = new char[n];
		for (int i = 0; i < n; i++) {
			as[i] = IO.nextChar();
		}
		return as;
	}

	static String[][] nss2(int n, int m) {
		String[][] as = new String[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.next();
			}
		}
		return as;
	}

	static int[][] nis2(int n, int m) {
		int[][] as = new int[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextInt();
			}
		}
		return as;
	}

	static long[][] nls2(int n, int m) {
		long[][] as = new long[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextLong();
			}
		}
		return as;
	}

	static double[][] nds2(int n, int m) {
		double[][] as = new double[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextDouble();
			}
		}
		return as;
	}

	static char[][] ncs2(int n, int m) {
		char[][] as = new char[n][m];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				as[i][j] = IO.nextChar();
			}
		}
		return as;
	}

	static int parseInt(String val) {
		return Integer.parseInt(val);
	}

	static int parseInt(char val) {
		return Integer.parseInt(String.valueOf(val));
	}

	static long parseLong(String val) {
		return Long.parseLong(val);
	}

	public static void main(String[] args) {
		try {
			solve();
			IO.flush();
		} catch (NumberFormatException e) {
			e.printStackTrace();
		}
	}
}

final class IO {
	private static final InputStream in = System.in;
	private static final PrintWriter out = new PrintWriter(System.out, false);
	private static final byte[] buffer = new byte[1024];
	private static int ptr = 0;
	private static int len = 0;

	private static boolean hasNextByte() {
		if (ptr < len)
			return true;
		ptr = 0;
		try {
			len = in.read(buffer);
		} catch (IOException e) {
			e.printStackTrace();
		}
		return len > 0;
	}

	private static int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	static boolean hasNext() {
		byte c;
		while (hasNextByte() && ((c = buffer[ptr]) < '!' || c > '~'))
			ptr++;
		return hasNextByte();
	}

	static String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (b >= '!' && b <= '~') {
			sb.append((char) b);
			b = readByte();
		}
		return sb.toString();
	}

	static char nextChar() {
		if (!hasNext())
			throw new NoSuchElementException();
		return (char) readByte();
	}

	static long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			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 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static int nextInt() {
		if (!hasNext())
			throw new NoSuchElementException();
		int n = 0;
		int sign = 1;
		int b = readByte();
		if (b == '-') {
			sign = -1;
			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 || b < '!' || b > '~')
				return n * sign;
			else
				throw new NumberFormatException();
			b = readByte();
		}
	}

	static double nextDouble() {
		return Double.parseDouble(next());
	}

	static void out(String val) {
		out.println(val);
	}

	static void flush() {
		out.flush();
	}
}

class PQE { // Priority Queue Entry
}

@SuppressWarnings("unchecked")
class PQ<A> { // Priority Queue
	private static class E extends PQE { // Entry
		Object a;
		int index;

		public E(Object a, int index) {
			this.a = a;
			this.index = index;
		}
	}

	private int n;
	private E[] as;
	private Comparator<A> comp;

	PQ(Comparator<A> comp) {
		this.comp = comp;
		as = new E[64];
		n = 1;
	}

	PQE add(A a) {
		E res = addEntry(a);
		fixUp(n - 1);
		return res;
	}

	A pop() {
		int max = n - 1;
		if (max == 0)
			return null;
		if (max == 1) {
			return removeLast();
		}

		E tmp = as[1];
		as[1] = as[max];
		as[max] = tmp;
		as[1].index = 1;
		as[max].index = max;

		A res = removeLast();
		fixDown(1);
		return res;
	}

	A get(PQE e) {
		return (A) ((E) e).a;
	}

	void remove(PQE e) {
		int k = ((E) e).index;
		int max = n - 1;
		if (k == max) {
			removeLast();
			return;
		}

		E tmp = as[k];
		as[k] = as[max];
		as[max] = tmp;
		as[k].index = k;
		as[max].index = max;

		removeLast();
		if (!fixDown(k))
			fixUp(k);
	}

	void update(PQE e, A a) {
		int k = ((E) e).index;
		as[k].a = a;
		if (!fixDown(k))
			fixUp(k);
	}

	boolean isEmpty() {
		return n == 1;
	}

	private A removeLast() {
		n--;
		E res = as[n];
		res.index = -1;
		as[n] = null;
		return (A) res.a;
	}

	private boolean fixUp(int k) {
		boolean res = false;
		while (k > 1) {
			int nk = k >> 1;
			if (comp.compare((A) as[k].a, (A) as[nk].a) < 0) {
				E tmp = as[k];
				as[k] = as[nk];
				as[nk] = tmp;
				as[k].index = k;
				as[nk].index = nk;
				k = nk;
				res = true;
				continue;
			}
			break;
		}
		return res;
	}

	private boolean fixDown(int k) {
		boolean res = false;
		while (k << 1 < n) {
			A a = (A) as[k].a;
			A l = (A) as[k << 1].a;
			if (k << 1 == n - 1) {
				if (comp.compare(a, l) <= 0)
					break;
				res = true;
				E tmp = as[k];
				as[k] = as[k << 1];
				as[k << 1] = tmp;
				as[k].index = k;
				as[k << 1].index = k << 1;
				break;
			}
			A r = (A) as[k << 1 | 1].a;
			if (comp.compare(a, l) <= 0 && comp.compare(a, r) <= 0)
				break;
			res = true;
			if (comp.compare(l, r) < 0) {
				int nk = k << 1;
				E tmp = as[k];
				as[k] = as[nk];
				as[nk] = tmp;
				as[k].index = k;
				as[nk].index = nk;
				k = nk;
			} else {
				int nk = k << 1 | 1;
				E tmp = as[k];
				as[k] = as[nk];
				as[nk] = tmp;
				as[k].index = k;
				as[nk].index = nk;
				k = nk;
			}
		}
		return res;
	}

	private E addEntry(A a) {
		if (n == as.length) {
			as = U.doubleSize(as);
		}
		return as[n] = new E(a, n++);
	}

	public String toString() {
		if (n == 1)
			return "[]";
		String s = null;
		for (int i = 1; i < n; i++) {
			A a = (A) as[i].a;
			if (s == null)
				s = "[" + a;
			else
				s += ", " + a;
		}
		return s + "]";
	}
}

interface F1<A> {
	A f();
}

interface F2<A, B> {
	B f(A a);
}

interface F3<A, B, C> {
	C f(A a, B b);
}

interface F4<A, B, C, D> {
	D f(A a, B b, C c);
}

interface F5<A, B, C, D, E> {
	E f(A a, B b, C c, D d);
}

interface F1V<A> {
	void f(A a);
}

interface F2V<A, B> {
	void f(A a, B b);
}

interface F3V<A, B, C> {
	void f(A a, B b, C c);
}

interface F4V<A, B, C, D> {
	void f(A a, B b, C c, D d);
}

interface F5V<A, B, C, D, E> {
	void f(A a, B b, C c, D d, E e);
}

class U { // Utilities
	static <A> ArrayList<A> make(int n, F2<Integer, A> maker) {
		ArrayList<A> res = new ArrayList<A>();
		for (int i = 0; i < n; i++)
			res.add(maker.f(i));
		return res;
	}

	static <A> ArrayList<A> filter(ArrayList<A> as, F2<A, Boolean> pred) {
		ArrayList<A> res = new ArrayList<A>();
		for (A a : as)
			if (pred.f(a))
				res.add(a);
		return res;
	}

	static <A> int count(ArrayList<A> as, F2<A, Boolean> pred) {
		int res = 0;
		for (A a : as)
			if (pred.f(a))
				res++;
		return res;
	}

	static <A> ArrayList<A> concat(ArrayList<A> as, ArrayList<A> bs) {
		ArrayList<A> res = new ArrayList<A>();
		res.addAll(as);
		res.addAll(bs);
		return res;
	}

	static <A> boolean any(ArrayList<A> as, F2<A, Boolean> pred) {
		for (A a : as)
			if (pred.f(a))
				return true;
		return false;
	}

	static <A> boolean all(ArrayList<A> as, F2<A, Boolean> pred) {
		for (A a : as)
			if (!pred.f(a))
				return false;
		return true;
	}

	static <A> ArrayList<A> flatten(ArrayList<ArrayList<A>> ass) {
		ArrayList<A> res = new ArrayList<A>();
		for (ArrayList<A> as : ass)
			res.addAll(as);
		return res;
	}

	static <A, B> B foldl(ArrayList<A> as, F3<B, A, B> f, B e) {
		B res = e;
		for (A a : as)
			res = f.f(res, a);
		return res;
	}

	static <A, B> B foldr(ArrayList<A> as, F3<A, B, B> f, B e) {
		B res = e;
		for (int i = as.size() - 1; i >= 0; i--)
			res = f.f(as.get(i), res);
		return res;
	}

	static <A> ArrayList<A> reverse(ArrayList<A> as) {
		int size = as.size();
		return make(size, i -> as.get(size - 1 - i));
	}

	static <A> void forEach(ArrayList<A> as, F1V<A> f) {
		for (A a : as)
			f.f(a);
	}

	static <A extends Comparable<A>> UP<TreeMap<A, Integer>, ArrayList<A>> compress(ArrayList<A> as) {
		TreeSet<A> set = new TreeSet<A>(as);
		TreeMap<A, Integer> map = new TreeMap<A, Integer>();
		ArrayList<A> imap = new ArrayList<A>();
		int i = 0;
		for (A a : set) {
			map.put(a, i++);
			imap.add(a);
		}
		return UP.make(map, imap);
	}

	static <A, B> ArrayList<B> map(ArrayList<A> as, F2<A, B> f) {
		return make(as.size(), (i) -> f.f(as.get(i)));
	}

	static <A, B> ArrayList<UP<A, B>> zip(ArrayList<A> as, ArrayList<B> bs) {
		return make(min(as.size(), bs.size()), (i) -> UP.make(as.get(i), bs.get(i)));
	}

	static <A extends Comparable<A>> A min(A a, A b) {
		return a.compareTo(b) < 0 ? a : b;
	}

	static <A extends Comparable<A>> A max(A a, A b) {
		return a.compareTo(b) > 0 ? a : b;
	}

	static <A extends Comparable<A>> A clamp(A a, A min, A max) {
		return a.compareTo(min) < 0 ? min : a.compareTo(max) > 0 ? max : a;
	}

	static <A> ArrayList<A> toAL(A[] as) {
		return make(as.length, i -> as[i]);
	}

	static <A> A[] doubleSize(A[] as) {
		return Arrays.copyOf(as, as.length << 1);
	}
}

class Rev<A extends Comparable<A>> implements Comparable<Rev<A>> {
	A a;

	Rev(A a) {
		this.a = a;
	}

	static <A extends Comparable<A>> Rev<A> make(A a) {
		return new Rev<A>(a);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof Rev))
			return false;
		Rev<?> r = (Rev<?>) o;
		return a == null ? r.a == null : a.equals(r.a);
	}

	public int compareTo(Rev<A> o) {
		return -a.compareTo(o.a);
	}

	public String toString() {
		return "-(" + a.toString() + ")";
	}
}

class Flat<A> implements Comparable<Flat<A>> {
	A a;

	Flat(A a) {
		this.a = a;
	}

	static <A> Flat<A> make(A a) {
		return new Flat<A>(a);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof Flat))
			return false;
		Flat<?> r = (Flat<?>) o;
		return a == null ? r.a == null : a.equals(r.a);
	}

	public int compareTo(Flat<A> o) {
		return 0;
	}

	public String toString() {
		return "0(" + a.toString() + ")";
	}
}

class UP<A, B> { // Unordered Pair
	A a;
	B b;

	UP(A a, B b) {
		this.a = a;
		this.b = b;
	}

	static <A, B> UP<A, B> make(A a, B b) {
		return new UP<A, B>(a, b);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof UP))
			return false;
		UP<?, ?> p = (UP<?, ?>) o;
		boolean aok = a == null ? p.a == null : a.equals(p.a);
		boolean bok = b == null ? p.b == null : b.equals(p.b);
		return aok && bok;
	}

	public String toString() {
		return "(" + a.toString() + ", " + b.toString() + ")";
	}
}

class P<A extends Comparable<A>, B extends Comparable<B>> extends UP<A, B> implements Comparable<P<A, B>> { // Pair
	P(A a, B b) {
		super(a, b);
	}

	static <A extends Comparable<A>, B extends Comparable<B>> P<A, B> make(A a, B b) {
		return new P<A, B>(a, b);
	}

	public int compareTo(P<A, B> o) {
		int sa = a.compareTo(o.a);
		int sb = b.compareTo(o.b);
		return sa != 0 ? sa : sb;
	}
}

class UT<A, B, C> { // Unordered Tuple
	A a;
	B b;
	C c;

	UT(A a, B b, C c) {
		this.a = a;
		this.b = b;
		this.c = c;
	}

	static <A, B, C> UT<A, B, C> make(A a, B b, C c) {
		return new UT<A, B, C>(a, b, c);
	}

	public boolean equals(Object o) {
		if (o == this)
			return true;
		if (!(o instanceof UT))
			return false;
		UT<?, ?, ?> t = (UT<?, ?, ?>) o;
		boolean aok = a == null ? t.a == null : a.equals(t.a);
		boolean bok = b == null ? t.b == null : b.equals(t.b);
		boolean cok = c == null ? t.c == null : c.equals(t.c);
		return aok && bok && cok;
	}

	public String toString() {
		return "(" + a.toString() + ", " + b.toString() + ", " + c.toString() + ")";
	}
}

class T<A extends Comparable<A>, B extends Comparable<B>, C extends Comparable<C>> extends UT<A, B, C> implements
		Comparable<T<A, B, C>> { // Tuple
	T(A a, B b, C c) {
		super(a, b, c);
	}

	static <A extends Comparable<A>, B extends Comparable<B>, C extends Comparable<C>> T<A, B, C> make(A a, B b, C c) {
		return new T<A, B, C>(a, b, c);
	}

	public int compareTo(T<A, B, C> o) {
		int sa = a.compareTo(o.a);
		int sb = b.compareTo(o.b);
		int sc = c.compareTo(o.c);
		return sa != 0 ? sa : sb != 0 ? sb : sc;
	}
}