Limak has a string S, that consists of N lowercase English letters.
Limak then created a new string by repeating S exactly K times.
For example, for S = "abcb" and K = 2, he would get "abcbabcb".
Your task is to count the number of subsequences "ab" (not necessarily consecutive) in the new string.
In other words, find the number pairs of indices i < j, such that the i-th and j-th characters in the new string are 'a' and 'b' respectively.

-----Input-----
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains two integers N and K, denoting the length of the initial string S and the number of repetitions respectively.
The second line contains a string S.
Its length is exactly N, and each of its characters is a lowercase English letter.

-----Output-----
For each test case, output a single line containing one integer — the number of subsequences "ab" in the new string.
For the given constraints, it can be proved that the answer fits in the 64-bit signed type.

-----Constraints-----
- 1 ≤ T ≤ 10
- 1 ≤ N ≤ 105
- 1 ≤ N * K ≤ 109 (in other words, the new string has length up to 109)

-----Example-----
Input:
3
4 2
abcb
7 1
aayzbaa
12 80123123
abzbabzbazab

Output:
6
2
64197148392731290

-----Explanation-----
Test case 1. Limak repeated the string "abcb" 2 times, and so he got "abcbabcb". There are 6 occurrences of the subsequence "ab":
- ABcbabcb (the two letters marked uppercase)
- AbcBabcb
- AbcbaBcb
- AbcbabcB
- abcbABcb
- abcbAbcB
Test case 2. Since K = 1, the new string is equal to the given S ("aayzbaa"). There are 2 occurrences of the subsequence "ab" in this string: AayzBaa and aAyzBaa.

```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 = "# cook your dish here\nT = int(input())\nwhile T != 0:\n\tT = T-1\n\tN,K = map(int,input().split())\n\tS = input()\n\tS1 = S+S\n\tsub = 'ab'\n\tlookup = [[0]*(2*N+1) for _ in range(3)]\n\tfor i in range(0,(2*N+1)):\n\t\tlookup[0][i] = 1\n\t#print(lookup)\n\tfor i in range(1,(2*N+1)):\n\t\tfor j in range(1,3):\n\t\t\tif S1[i-1] == sub[j-1]:\n\t\t\t\tlookup[j][i] = lookup[j-1][i-1] + lookup[j][i-1]\n\t\t\telse:\n\t\t\t\tlookup[j][i] = lookup[j][i-1]\n\t#print(lookup)\n\tbase = lookup[2][N]\n\t#print('base='+str(base))\n\tinc = lookup[2][2*N] - 2*base\n\t#print('inc='+str(inc))\n\tans = K*base + ((K-1)*(K)*inc)//2\n\tprint(ans)\n\t"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13429