Problem: On a number line there are n balls. At time moment 0 for each ball the following data is known: its coordinate xi, speed vi (possibly, negative) and weight mi. The radius of the balls can be ignored.

The balls collide elastically, i.e. if two balls weighing m1 and m2 and with speeds v1 and v2 collide, their new speeds will be: 

<image>.

Your task is to find out, where each ball will be t seconds after.

Input

The first line contains two integers n and t (1 ≤ n ≤ 10, 0 ≤ t ≤ 100) — amount of balls and duration of the process. Then follow n lines, each containing three integers: xi, vi, mi (1 ≤ |vi|, mi ≤ 100, |xi| ≤ 100) — coordinate, speed and weight of the ball with index i at time moment 0.

It is guaranteed that no two balls have the same coordinate initially. Also each collision will be a collision of not more than two balls (that is, three or more balls never collide at the same point in all times from segment [0;t]).

Output

Output n numbers — coordinates of the balls t seconds after. Output the numbers accurate to at least 4 digits after the decimal point.

Examples

Input

2 9
3 4 5
0 7 8


Output

68.538461538
44.538461538


Input

3 10
1 2 3
4 -5 6
7 -8 9


Output

-93.666666667
-74.666666667
-15.666666667

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.StringTokenizer;


public class Main {
    static final double EPS = 1e-9;

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = sc.nextInt();
        int T = sc.nextInt();
        Ball[] balls = new Ball[n];
        for (int i = 0; i < n; i++)
            balls[i] = new Ball(sc.nextInt(), sc.nextInt(), sc.nextInt());
        double time = 0;
        while (time < T) {
            double t = 1e5;
            for (int i = 0; i < n; i++)
                for (int j = i + 1; j < n; j++) {
                    double collisionTime = (balls[j].x - balls[i].x) / (balls[i].v - balls[j].v);
                    if (collisionTime >= EPS) t = Math.min(t, collisionTime);
                }
            if (time + t > T || t == 0) break;
            time += t;
            for (Ball b : balls)
                b.setX(t);
            boolean collided[] = new boolean[n];
            for (int i = 0; i < n; i++) {
                if (collided[i]) continue;
                for (int j = i + 1; j < n; j++) {
                    if (collided[j]) continue;
                    if (Math.abs(balls[i].x - balls[j].x) <= EPS) {
                        double m1 = balls[i].m, m2 = balls[j].m, v1 = balls[i].v, v2 = balls[j].v;
                        balls[i].v = getNewV(m1, m2, v1, v2);
                        balls[j].v = getNewV(m2, m1, v2, v1);
                        collided[i] = true;
                        collided[j] = true;
                    }
                }
            }
        }
        double rem = T - time;
        for (Ball b : balls) {
            b.setX(rem);
            out.println(b.x);
        }

        out.flush();
        out.close();
    }

    static double getNewV(double m1, double m2, double v1, double v2) {
        return ((m1 - m2) * v1 + 2 * m2 * v2) / (m1 + m2);
    }

    static class Ball {
        double x, v, m;

        public Ball(double x, double v, double m) {
            this.x = x;
            this.v = v;
            this.m = m;
        }

        void setX(double t) {
            x = x + t * v;
        }

        @Override
        public String toString() {
            return "Ball{" +
                    "x=" + x +
                    ", v=" + v +
                    ", m=" + m +
                    '}';
        }
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }


        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }


        public int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public long[] nextLongArray(int n) throws IOException {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }


        public Integer[] nextIntegerArray(int n) throws IOException {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public double[] nextDoubleArray(int n) throws IOException {
            double[] ans = new double[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextDouble();
            return ans;
        }

        public short nextShort() throws IOException {
            return Short.parseShort(next());
        }

    }

}