import sys

sys.setrecursionlimit(200005)
# sys.set_int_max_str_digits(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()

dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
# inf = -1-(-1 << 31)
inf = -1-(-1 << 62)

# md = 10**9+7
md = 998244353

# 偶数長、奇数長含めて回文「直径」（つまり全長）を返す
# s[i]の前の隙間を中心とした回文長がres[i*2]（偶数長）
# s[i]を中心とした回文長がres[i*2+1]（奇数長）
#  a b a a b a
# 0103016103010
# dummyがsに入っていないか注意
def Manacher(s):
    dummy="@"
    s = dummy + dummy.join(s) + dummy
    i=j=0
    res=[-1]*len(s)
    while i<len(s):
        while i-j>=0 and i+j<len(s) and s[i-j]==s[i+j]:j+=1
        res[i]=j-1
        k=1
        while i-k>=0 and k+res[i-k]+1<j:
            res[i+k]=res[i-k]
            k+=1
        i+=k
        j-=k
    return res

def solve():
    n,m=LI()
    s=SI()
    ll=Manacher(s)
    if max(ll)>=m:
        print(1)
    elif ll[n]==n:
        print((m+n-1)//n)
    else:
        mn=inf
        rr=Manacher(s[::-1])
        for i in range(n):
            if ll[i]+rr[n-i]==n:
                mn=min(mn,i,n-i)
        if mn==inf:
            print(-1)
        else:
            # print(mn)
            # cn-mn>=m
            # c>=(m+mn)/n
            print((m+mn+n-1)//n)

for _ in range(II()):solve()