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.*;
import java.util.*;

public class Test {

    static int readInt() {
        int ans = 0;
        boolean neg = false;
        try {
            boolean start = false;
            for (int c = 0; (c = System.in.read()) != -1; ) {
                if (c == '-') {
                    start = true;
                    neg = true;
                    continue;
                } else if (c >= '0' && c <= '9') {
                    start = true;
                    ans = ans * 10 + c - '0';
                } else if (start) break;
            }
        } catch (IOException e) {
        }
        return neg ? -ans : ans;
    }

    static long readLong() {
        long ans = 0;
        boolean neg = false;
        try {
            boolean start = false;
            for (int c = 0; (c = System.in.read()) != -1; ) {
                if (c == '-') {
                    start = true;
                    neg = true;
                    continue;
                } else if (c >= '0' && c <= '9') {
                    start = true;
                    ans = ans * 10 + c - '0';
                } else if (start) break;
            }
        } catch (IOException e) {
        }
        return neg ? -ans : ans;
    }

    static String readLine() {
        StringBuilder b = new StringBuilder();
        try {
            boolean start = false;
            for (int c = 0; (c = System.in.read()) != -1; ) {
                if (Character.isLetterOrDigit(c)) {
                    start = true;
                    b.append((char)c);
                } else if (start) break;
            }
        } catch (IOException e) {
        }
        return b.toString();
    }

    static PrintWriter writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

    int N = 3456789;
    long[] add = new long[N];

    void updSum(int i, int ll, int rr, int a, int b, long v) {
        if (rr < a || ll > b) return;
        if (ll == rr) {
            add[i] += v;
            return;
        }
        if (a <= ll && rr <= b) {
            add[i] += v;
            return;
        }
        pushSum(i);
        int mid = (ll + rr) / 2;
        updSum(i+i, ll, mid, a, b, v);
        updSum(i+i+1, mid+1, rr, a, b, v);
    }

    long findSum(int i, int ll, int rr, int j) {
        if (j < ll | j > rr) return 0;
        if (ll == rr) return add[i];
        pushSum(i);
        int mid = (ll + rr) / 2;
        return findSum(i+i, ll, mid, j) + findSum(i+i+1, mid + 1, rr, j);
    }

    void pushSum(int i) {
        if (add[i] != 0) {
            add[i+i] += add[i];
            add[i+i+1] += add[i];
            add[i] = 0;
        }
    }

    void start() {
        int n = readInt();
        int w = readInt();
        for (int i = 0; i < n; i++) {
            int L = readInt();
            int[] a = new int[L+2];
            for (int j = 1; j <= L; j++) a[j] = readInt();
            List<int[]> ids = new ArrayList<>();
            for (int j = 1; j <= L; j++) {
                ids.add(new int[]{j, j});
                ids.add(new int[]{j + w - L + 1, -j});
            }
            if (w - L > 0) {
                ids.add(new int[]{1, L + 1});
                ids.add(new int[]{w - L + 1, -L - 1});
                ids.add(new int[]{L + 1, L + 1});
                ids.add(new int[]{w + 1, -L - 1});
            }
            Collections.sort(ids, (x, y) -> {
                if (x[0] == y[0]) return Integer.compare(x[1], y[1]);
                else return Integer.compare(x[0], y[0]);
            });
            TreeMap<Integer, Integer> max = new TreeMap<>();
            int pmax = 0;
            int begin = 1;
            for (int[] e : ids) {
                int p = e[0], j = e[1];
                if (j > 0) max.put(a[j], max.getOrDefault(a[j], 0) + 1);
                else {
                    int v = max.get(a[-j]);
                    if (v > 1) max.put(a[-j], v - 1);
                    else max.remove(a[-j]);
                }
                if (begin == p && !max.isEmpty()) pmax = max.lastKey();
                if (p > begin && (max.isEmpty() || pmax != max.lastKey())) {
                    updSum(1, 1, w, begin, p - 1, pmax);
                    begin = p;
                    pmax = max.isEmpty() ? Integer.MIN_VALUE : max.lastKey();
                }
            }
        }

        for (int i = 0; i < w; i++) {
            long v = findSum(1, 1, w, i+1);

            writer.print(v + " ");
        }
    }

    public static void main(String[] args) {
        Test te = new Test();
        te.start();
        writer.flush();
    }
}