read_line.to_i.times do
  puts solve()
end

def solve
  n, m = read_line.split.map(&.to_i)
  s = read_line.chars
  r = manacher(s)
  max = 0
  (n * 2).times do |i|
    if i % 2 == 1
      len = (r[i] + 1) // 2
      max = {max, len * 2 - 1}.max
    else
      len = r[i] // 2
      max = {max, len * 2}.max
    end
  end
  return 1 if m <= max

  r = manacher(s + s)
  max = 0
  rep = false
  (n * 4).times do |i|
    next if !(i - r[i] <= 2 * n && 2 * n <= i + r[i])
    if i % 2 == 1
      len = (r[i] + 1) // 2
      if len * 2 - 1 > max
        max = len * 2 - 1
        rem = s[..(i // 2 - len)]
        if rem == rem.reverse
          rep = true
        end
      end
    else
      len = r[i] // 2
      if len * 2 > max
        max = len * 2
        rem = s[..(i // 2 - 1 - len)]
        if rem == rem.reverse
          rep = true
        end
      end
    end
  end
  # puts [r, max, rep]
  return 2 if m <= max
  if rep
    (m - max + n - 1) // n + 2
  else
    -1
  end
end

def manacher(s)
  str = ['$']
  s.each do |c|
    str << c << '$'
  end
  i = 0
  j = 0
  rad = Array.new(str.size, 0)
  while i < str.size
    while i - j >= 0 && i + j < str.size && str[i - j] == str[i + j]
      j += 1
    end
    rad[i] = j
    k = 1
    while k <= i && k + rad[i - k] < j
      rad[i + k] = rad[i - k]
      k += 1
    end
    i += k
    j -= k
  end
  rad

  # pos = 1.step(to: str.size - 1, by: 2).max_by { |i| rad[i] }
  # len = (rad[pos] + 1) // 2
  # odd_max = {(pos - rad[pos] + 1) // 2, len * 2 - 1}

  # pos = 0.step(to: str.size - 1, by: 2).max_by { |i| rad[i] }
  # len = rad[pos] // 2
  # even_max = {(pos - rad[pos] + 1) // 2, len * 2}
end