Problem: You are given n arrays that can have different sizes. You also have a table with w columns and n rows. The i-th array is placed horizontally in the i-th row. You can slide each array within its row as long as it occupies several consecutive cells and lies completely inside the table.

You need to find the maximum sum of the integers in the j-th column for each j from 1 to w independently.

<image> Optimal placements for columns 1, 2 and 3 are shown on the pictures from left to right.

Note that you can exclude any array out of a column provided it remains in the window. In this case its value is considered to be zero.

Input

The first line contains two integers n (1 ≤ n ≤ 10^{6}) and w (1 ≤ w ≤ 10^{6}) — the number of arrays and the width of the table.

Each of the next n lines consists of an integer l_{i} (1 ≤ l_{i} ≤ w), the length of the i-th array, followed by l_{i} integers a_{i1}, a_{i2}, …, a_{il_i} (-10^{9} ≤ a_{ij} ≤ 10^{9}) — the elements of the array.

The total length of the arrays does no exceed 10^{6}.

Output

Print w integers, the i-th of them should be the maximum sum for column i.

Examples

Input


3 3
3 2 4 8
2 2 5
2 6 3


Output


10 15 16 


Input


2 2
2 7 8
1 -8


Output


7 8 

Note

Illustration for the first example is in the statement.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.IOException;
import java.util.Random;
import java.io.InputStreamReader;
import java.util.TreeMap;
import java.io.BufferedReader;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author null
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Input in = new Input(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        long[] max;
        long sum;

        public void solve(int testNumber, Input in, PrintWriter out) {
            try {
                int n = in.readInt();
                int w = in.readInt();
                int[][] a = new int[n][];
                for (int i = 0; i < n; i++) {
                    int L = in.readInt();
                    a[i] = new int[L];
                    for (int j = 0; j < L; j++) {
                        a[i][j] = in.readInt();
                    }
                }

                Rand.shuffle(a);
                Arrays.sort(a, Comparator.comparing(arr -> -arr.length));
                TreeMap<Integer, Integer>[] maps = new TreeMap[n];
                for (int i = 0; i < n; i++) {
                    maps[i] = new TreeMap<>();
                }
                max = new long[n];
                sum = 0;

                StringBuilder ans = new StringBuilder();
                for (int i = 0; i < w; i++) {
                    for (int j = 0; j < n; j++) {
                        boolean zero = (a[j].length <= i) || (i + a[j].length < w);
                        if (a[j].length > i) {
                            add(maps[j], a[j][i], j, zero);
                        } else {
                            break;
                        }
                    }

                    for (int j = 0; j < n; j++) {
                        boolean zero = (a[j].length <= i) || (i + a[j].length < w);
                        int pos = a[j].length - (w - i) - 1;
                        if (pos >= 0) {
                            remove(maps[j], a[j][pos], j, zero);
                        } else {
                            break;
                        }
                    }
                    ans.append(sum).append(' ');
                }
                out.println(ans.toString());
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }

        void add(TreeMap<Integer, Integer> map, int key, int i, boolean zero) {
            Integer oldValue = map.get(key);
            if (oldValue == null) {
                map.put(key, 1);
            } else {
                map.put(key, oldValue + 1);
            }

            int newMax = zero ? Math.max(map.lastKey(), 0) : map.lastKey();
            if (newMax != max[i]) {
                sum += (newMax - max[i]);
                max[i] = newMax;
            }
        }

        void remove(TreeMap<Integer, Integer> map, int key, int i, boolean zero) {
            int oldValue = map.get(key);
            if (oldValue == 1) {
                map.remove(key);
            } else {
                map.put(key, oldValue - 1);
            }

            int newMax = zero ? Math.max(map.lastKey(), 0) : map.lastKey();
            if (newMax != max[i]) {
                sum += (newMax - max[i]);
                max[i] = newMax;
            }

        }

    }

    static class Rand {
        public static final Random INSTANCE = new Random();

        public static void shuffle(int[][] a) {
            for (int i = 0; i + 1 < a.length; i++) {
                int p = INSTANCE.nextInt(a.length - i);
                int[] t = a[i];
                a[i] = a[p];
                a[p] = t;
            }
        }

    }

    static class Input {
        public final BufferedReader reader;
        private String line = "";
        private int pos = 0;

        public Input(InputStream inputStream) {
            reader = new BufferedReader(new InputStreamReader(inputStream));
        }

        private boolean isSpace(char ch) {
            return ch <= 32;
        }

        public String readWord() throws IOException {
            skip();
            int start = pos;
            while (pos < line.length() && !isSpace(line.charAt(pos))) {
                pos++;
            }
            return line.substring(start, pos);
        }

        public int readInt() throws IOException {
            return Integer.parseInt(readWord());
        }

        private void skip() throws IOException {
            while (true) {
                if (pos >= line.length()) {
                    line = reader.readLine();
                    pos = 0;
                }
                while (pos < line.length() && isSpace(line.charAt(pos))) {
                    pos++;
                }
                if (pos < line.length()) {
                    return;
                }
            }
        }

    }
}