import sys
input = lambda :sys.stdin.readline()[:-1]
ni = lambda :int(input())
na = lambda :list(map(int,input().split()))
yes = lambda :print("yes");Yes = lambda :print("Yes");YES = lambda : print("YES")
no = lambda :print("no");No = lambda :print("No");NO = lambda : print("NO")
#######################################################################
def manacher(s):
    s = s.replace('', '#')
    n = len(s)
    p = [1 for _ in range(n)]
    c = 0
    for i in range(1, n):
        if i < c + p[c]:
            p[i] = min(p[c - (i - c)], c + p[c] - i)
        while i - p[i] >= 0 and i + p[i] < n and s[i - p[i]] == s[i + p[i]]:
            p[i] += 1
        if i + p[i] > c + p[c]:
            c = i
    return p

def max_palindrome(s):
    P = manacher(s)
    return max(P) - 1

def solve(n, m, s):
    A = max_palindrome(s)
    B = max_palindrome(s + s)
    C = max_palindrome(s + s + s)
    if A >= m:
        return 1
    elif B >= m:
        return 2
    elif C >= m:
        return 3
    elif B == C and B < m:
        return -1
    else:
        return 3 + (m - B - 1) // (C - B)

def greedy(n, m, s):
    z = ""
    for t in range(1000):
        if max_palindrome(z) >= m:
            return t
        z += s
    return -1


for _ in range(ni()):
    n, m = na()
    s = input()
    print(solve(n, m, s))
    #print(greedy(n, m, s))


# from random import randint
# for _ in range(10000):
#     n = randint(1, 10)
#     m = randint(1, n * 10)
#     s = "".join([chr(randint(97, 122)) for _ in range(n)])
#     if solve(n, m, s) != greedy(n, m, s):
#         print(n, m)
#         print(s)
#         print(solve(n, m, s))
#         print(greedy(n, m, s))
#         break
#     #print(_)

# n, m = na()
# s = input()
# print(solve(n, m, s))
# z = s
# for i in range(4):
#     print(*manacher(z))
#     z += s