You are given an array A with size N (indexed from 0) and an integer K. Let's define another array B with size N · K as the array that's formed by concatenating K copies of array A.
For example, if A = {1, 2} and K = 3, then B = {1, 2, 1, 2, 1, 2}.
You have to find the maximum subarray sum of the array B. Fomally, you should compute the maximum value of Bi + Bi+1 + Bi+2 + ... + Bj, where 0 ≤ i ≤ j < N · K.

-----Input-----

- The first line of the input contains a single integer T denoting the number of test cases. The description of T test cases follows.
- The first line of each test case contains two space-separated integers N and K.
- The second line contains N space-separated integers A0, A1, ..., AN-1.

-----Output-----
For each test case, print a single line containing the maximum subarray sum of B.

-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 105
- 1 ≤ K ≤ 105
- -106 ≤ Ai ≤ 106 for each valid i

-----Subtasks-----
Subtask #1 (18 points): N · K ≤ 105
Subtask #2 (82 points): original constraints

-----Example-----
Input:

2
2 3
1 2
3 2
1 -2 1

Output:

9
2

-----Explanation-----
Example case 1: B = {1, 2, 1, 2, 1, 2} and the subarray with maximum sum is the whole {1, 2, 1, 2, 1, 2}. Hence, the answer is 9.
Example case 2: B = {1, -2, 1, 1, -2, 1} and the subarray with maximum sum is {1, 1}. Hence, the answer is 2.

```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 = 'def kadane(l):\r\n\tcurrent_sum,best_so_far=0,-9999999999999\r\n\tfor i in l:\r\n\t\tcurrent_sum+=i\r\n\t\tif best_so_far<current_sum:\r\n\t\t\tbest_so_far=current_sum\r\n\t\tif current_sum<0:\r\n\t\t\tcurrent_sum=0\r\n\treturn best_so_far\r\ndef max_sum(l,k):\r\n\tif k==1:\r\n\t\tans=kadane(l)\r\n\t\treturn ans\r\n\tcurrent_prefix_sum,best_prefix_sum=0,-99999999999999\r\n\tcurrent_postfix_sum,best_postfix_sum=0,-9999999999999\r\n\ttotal_sum=0\r\n\tfor i in l:\r\n\t\tcurrent_prefix_sum+=i\r\n\t\tbest_prefix_sum=max(current_prefix_sum,best_prefix_sum)\r\n\ttotal_sum=current_prefix_sum\r\n\tfor i in range(len(l)-1,-1,-1):\r\n\t\tcurrent_postfix_sum+=l[i]\r\n\t\tbest_postfix_sum=max(current_postfix_sum,best_postfix_sum)\r\n\tif total_sum<0:\r\n\t\tans=max(best_prefix_sum+best_postfix_sum,kadane(l))\r\n\telse:\r\n\t\tans=max(best_prefix_sum+best_postfix_sum+((k-2)*total_sum),kadane(l))\r\n\treturn ans\r\nt=int(input())\r\nwhile t>0:\r\n\tn,k=map(int,input().split())\r\n\tl=list(map(int,input().split()))\r\n\tprint(max_sum(l,k))\r\n\tt-=1'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13341