import sys
input = sys.stdin.readline

# Manacher
# https://snuke.hatenablog.com/entry/2014/12/02/235837

def maxpan(S2):
    T=[]
    for i in range(len(S2)):
        T.append(S2[i])
        T.append("!")

    T.pop()

    S=T

    LEN=len(S)
    i=0
    j=0
    R=[0]*LEN # 文字 i を中心とする最長の回文の半径

    while i<LEN:
        while i-j>=0 and i+j<LEN and S[i-j]==S[i+j]:
            j+=1
        R[i]=j
        
        k=1
        while i-k>=0 and i+k<LEN and k+R[i-k]<j:
            R[i+k]=R[i-k]
            k+=1

        i+=k
        j-=k

    MAX=0

    #print(R)

    for i in range(LEN):
        if i%2==0:
            if R[i]%2==0:
                MAX=max(MAX,R[i]-1)
            else:
                MAX=max(MAX,R[i])
        else:
            if R[i]%2==1:
                MAX=max(MAX,R[i]-1)
            else:
                MAX=max(MAX,R[i])
            

    return MAX
    


T=int(input())
for tests in range(T):
    N,M=map(int,input().split())
    S=list(input().strip())

    A=[maxpan(S),maxpan(S+S),maxpan(S+S+S)]

    if A[0]>=M:
        print(1)
        continue

    if A[1]>=M:
        print(2)
        continue

    if A[2]-A[1]==0:
        print(-1)
        continue

    f=A[1]
    plus=A[2]-A[1]

    # f+ plus*(x-1)>=M

    print((M-f+plus-1)//plus+2)