from sys import stdin
input = stdin.readline

def Manacher(S):
    C = [""]
    for s in S:
        C.append(s)
        C.append("")
    R = [0]*len(C)
    i = 0
    j = 0
    while i < len(C):
        while 0 <= i-j and i+j < len(C) and C[i-j] == C[i+j]:
            j += 1
        R[i] = j
        k = 1
        while 0 <= i-k and k+R[i-k] < j:
            R[i+k] = R[i-k]
            k += 1
        i += k
        j -= k
    odd = []
    even = []
    for i in range(1, len(C)-1):
        if i%2 == 1:
            odd.append(R[i]//2)
        else:
            even.append(R[i]//2)
    return odd, even

def func(S):
    odd, even = Manacher(S)
    MAX = -1
    for o in odd:
        MAX = max(MAX, o*2-1)
    for e in even:
        MAX = max(MAX, e*2)
    return MAX

for _ in range(int(input())):
    N, M = map(int, input().split())
    S = input().rstrip("\n")

    S2 = S+S
    S3 = S+S+S

    if M <= func(S):
        print(1)
        continue
    if M <= func(S2):
        print(2)
        continue

    if func(S2)+N == func(S3):
        s = func(S2)
        print(2+(M-s+N-1)//N)
    else:
        print(-1)