# 偶数長含めた回文の長さを求める
# R[2*i] = L: S[i]を中心とする奇数長の最大回文
# R[2*i+1] = L: S[i:i+2]を中心とする偶数長の最大回文
# ダミー文字を挟むが、各 R[i] は実際の回文の文字列長と一致する
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

import sys
input = sys.stdin.readline
T = int(input())
for _ in range(T):
    N, M = map(int, input().split())
    S = input().strip()
    a = manacher(S)
    ma = max(a)
    b = manacher(S+S)
    mb = max(b)
    if ma>=M:
        print(1)
        continue
    if mb>=M:
        print(2)
        continue
    if mb-ma==0:
        print(-1)
        continue
    cnt = (M-mb+mb-ma-1)//(mb-ma)
    print(cnt+2)