def manacher(S):
    C = []
    for a in S:
        C.append(a)
        C.append(0)
    C.pop()

    L = len(C)

    R = [0]*L

    i = j = 0
    while i < L:
        while j <= i < L-j and C[i-j] == C[i+j]:
            j += 1
        R[i] = j
        k = 1
        while j-R[i-k] > k <= i < L-k:
            R[i+k] = R[i-k]
            k += 1
        i += k; j -= k

    for i in range(L):
        if i & 1 == R[i] & 1:
            R[i] -= 1
    return R

def solve(N, M, S):
    R = manacher(S)
    if max(R) >= M:
        print(1)
        return
    R = manacher(S + S)
    if max(R) >= M:
        print(2)
        return
    ans = 2000000000
    for i in range(len(R)):
        if i % 2 == 0:
            if (R[i] + 1) // 2 + i // 2 == N + N and R[i] > N:
                M -= R[i] - N
                ans = min(ans, (M + N - 1) // N + 1)
        else:
            if (i + 1) // 2 + R[i] // 2 == N + N and R[i] > N:
                M -= R[i] - N
                ans = min(ans, (M + N - 1) // N + 1)
                
    if ans == 2000000000:
      print(-1)
    else:
      print(ans)
    return

T = int(input())
for _ in range(T):
    N, M = map(int, input().split())
    S = input()
    solve(N, M, S)