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 $n$ ($1 \le n \le 10^{6}$) and $w$ ($1 \le w \le 10^{6}$) — the number of arrays and the width of the table.

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

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'import sys\ninput = sys.stdin.readline\nfrom collections import deque\ndef slidemax(X, k):\n    q = deque([])\n    ret = []\n    for i in range(len(X)):\n        while q and q[-1][1] <= X[i]:\n            q.pop()\n        deque.append(q, (i+k, X[i]))\n        if q[0][0] == i:\n            deque.popleft(q)\n        if i >= k-1:\n            ret.append(q[0][1])\n    return ret\n \nN, W = list(map(int, input().split()))\nA = [0] * W\ns = 0\nfor _ in range(N):\n    l, *B = list(map(int, input().split()))\n    if l*2 < W:\n        C = slidemax([0]*(l-1)+B+[0]*(l-1), l)\n        m = max(B + [0])\n        s += m\n        for i in range(l-1):\n            A[i] += C[i] - m\n            A[-i-1] += C[-i-1] - m\n    else:\n        C = slidemax([0]*(W-l)+B+[0]*(W-l), W - l + 1)\n        A = [a+c for a, c in zip(A, C)]\n\nprint(*[a+s for a in A])\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14213