def walsh_hadamard_transform(f):
  k = (len(f) - 1).bit_length()
  h = 1
  for _ in range(k):
    for i in range(0, len(f), h * 2):
      for j in range(i, i + h):
        f[j], f[j + h] = f[j] + f[j + h], f[j] - f[j + h]
    h *= 2

def Xor_convolution(a, b):
  f = a[:]
  g = b[:]
  k = (len(f) - 1).bit_length()
  walsh_hadamard_transform(f)
  walsh_hadamard_transform(g)
  for i in range(1 << k):
    f[i] = f[i] * g[i]
  walsh_hadamard_transform(f)
  for i in range(len(f)):
    f[i] >>= k
  return f

N, K = map(int, input().split())
A = list(map(int, input().split()))
F = [0 for i in range(1 << 15)]
for a in A:
  F[a >> 15] += 1
F = Xor_convolution(F, F)
F[0] -= N
for i in range(1 << 15):
  F[i] //= 2
  if i > 0:
    F[i] += F[i - 1]

i = 0
while F[i] < K:
  i += 1

mask = i
ans = i << 15
if i > 0:
  K -= F[i - 1]

G = [[] for i in range(1 << 15)]
for a in A:
  b = a >> 15
  G[b].append(a - (b << 15))

F = [0 for i in range(1 << 15)]
for i in range(1 << 15):
  c = min(len(G[i]), len(G[mask ^ i]))
  if c <= 1024:
    for j in G[i]:
      for k in G[i ^ mask]:
        F[j ^ k] += 1
  else:
    f, g = [0 for _ in range(1 << 15)], [0 for _ in range(1 << 15)]
    for j in G[i]:
      f[j] += 1
    for k in G[i ^ mask]:
      g[k] += 1
    f = Xor_convolution(f, g)
    for j in range(1 << 15):
      F[j] += f[j]

if mask == 0:
  F[0] -= N
for i in range(1 << 15):
  F[i] //= 2
  if i > 0:
    F[i] += F[i - 1]

i = 0
while F[i] < K:
  i += 1
ans += i
print(ans)