class StrHash():
    def __init__(self,S):
        self.mod = 10**9+7
        Len=len(S)
        self.Power256 = [1] * (Len + 1)
        for i in range(Len):
             self.Power256[i + 1] = self.Power256[i] * 256 % self.mod
        S=[ord(S[i]) for i in range(Len)]
        self.H = [1] * (Len + 1)
        for i in range(Len):
            self.H[i + 1] = (self.H[i] * 256 + S[i]) % self.mod
    def getHash(self,l,r):
        if l>r:
            return 0
        return (self.H[r]-(self.Power256[r-l+1]*self.H[l-1]))%self.mod

def isok(pos,n):
    if pos+n>=N or pos-n<0:
        return False
    if sh.getHash(pos-n+1,pos+n+1) == sh_rev.getHash(N-1-(pos+n)+1,N-1-(pos-n)+1):
        return True
    return False

def isok2(pos,n):
    if pos-n+1<=0 or pos+n>N:
        return False
    if sh.getHash(pos-n+1,pos+n) == sh_rev.getHash(N+1-(pos+n),N+1-(pos-n+1)):
        return True
    return False

def is_r(l,r):
    if sh.getHash(l+1,r+1) == sh_rev.getHash(N+1-(r+1),N+1-(l+1)):
        return True
    return False

T=int(input())
for _ in range(T):
    N,M=map(int,input().split())
    S=input()
    sh=StrHash(S)
    sh_rev=StrHash(S[::-1])
    ans=10**20
    for i in range(N):
        left,right=0,10**10
        while right-left>1:
            mid=(right+left)//2
            if isok(i,mid):
                left=mid
            else:
                right=mid
        if left+1+left>=M:
            ans=1
            continue
    for i in range(1,N):
        left,right=0,10**10
        while right-left>1:
            mid=(right+left)//2
            if isok2(i,mid):
                left=mid
            else:
                right=mid
        if left+1+left>=M:
            ans=1
            continue
    for i in range(N-1):
        if is_r(0,i) and is_r(i+1,N-1):
            if M>=i and M>=N-1-i+1:
                a=i
                b=(N-1-i+1)
                ans=min(ans,-(-(M+a)//N))
                ans=min(ans,-(-(M+b)//N))
    for i in range(N-1):
        if is_r(0,N-1):
            if M<=N:
                ans=1
            else:
                ans=min(ans,-(-M//N))
    if ans==10**20:
        print(-1)
    else:
        print(ans)