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 maximum_subarray_sum(a):\n    N = len(a)\n    max_so_far = -float('inf')\n    max_ending_here = 0\n\n    start = 0\n    end = 0\n    s = 0\n    for i in range(N):\n        max_ending_here += a[i]\n        if(max_ending_here>max_so_far):\n            max_so_far = max_ending_here\n            start = s\n            end = i\n        if(max_ending_here<0):\n            max_ending_here = 0\n            s = i+1\n    return start,end\n\n# a = [-1,-2,-3,-4,-5]\n# print(maximum_subarray_sum(a))\n\nT = int(input())\nans = []\n\nfor _ in range(T):\n    N,K = [int(i) for i in input().split()]\n    A = [int(i) for i in input().split()]\n\n\n    if(K==1):\n        s,e = maximum_subarray_sum(A)\n        ans.append(sum(A[s:e+1]))\n    else:\n        s,e = maximum_subarray_sum(A+A)\n        # print('$',s,e,sum(A[2:3]))\n        if(e<N):\n            ans.append(sum(A[s:e+1]))\n        else:\n            e -= N\n            ans.append(sum(A[s:])+sum(A)*(K-2)+sum(A[:e+1]))\n\nfor i in ans:\n    print(i)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13599