Buggy python submission (verdict: Time Limit Exceeded):
import copy
N,K=list(map(int,input().split()))
a=list(map(int,input().split()))

num=0
a_sum=[0]
for i in range(N):
  num+=a[i]
  a_sum.append(num)
  

a_mat=[[0 for i in range(N)] for j in range(N)]
non_zero=[]
for i in range(N):
  for j in range(i,N):
    a_mat[i][j] = a_sum[j+1]-a_sum[i]
    non_zero.append([i,j])

a_mat2=copy.deepcopy(a_mat)

maxbit=1
while True:
  if a_sum[N]<2**maxbit and a_sum[N]>=2**(maxbit-1): 
    break
  else:
    maxbit+=1
maxnum=0
num_rest=int(N*(N+1)/2)
num_rest_now=int(N*(N+1)/2)
for bit in range(maxbit):
  non_zero2=[]
  for i, j in non_zero:
    if a_mat[i][j]&(2**(maxbit-bit-1)) == 0 and a_mat[i][j]!=0:
      num_rest_now-=1
      a_mat2[i][j]=0
    else:
      non_zero2.append([i,j])
  #print(non_zero)
  #print(a_mat)
  #print(num_rest_now)
  
  if num_rest_now >= K:
    maxnum+=2**(maxbit-bit-1)
    a_mat=copy.deepcopy(a_mat2)
    num_rest=num_rest_now
    non_zero=copy.deepcopy(non_zero2)
  else:
    a_mat2=copy.deepcopy(a_mat)
    num_rest_now=num_rest
    
  
  
print(maxnum)
    

Fixed submission:
import sys
from collections import deque, defaultdict
import copy
input=sys.stdin.readline
sys.setrecursionlimit(10 ** 9)

N, K = list(map(int, input().split()))
a = list(map(int, input().split()))
sum_a = [0, a[0]]
for i in range(1, N):
    sum_a.append(sum_a[-1]+a[i])

bubunwa = []
for i in range(N):
    for j in range(i + 1, N + 1):
        bubunwa.append(sum_a[j] - sum_a[i])

max_bit = 2
while True:
    if sum_a[-1] < 2**max_bit:
        break
    max_bit += 1

sum = 0
for i in range(max_bit ,-1, -1):
    kouho = []
    for n in bubunwa:
        if n & 2**i == 2**i:
            kouho.append(n)
    if len(kouho) >= K:
        bubunwa = copy.deepcopy(kouho)
        sum += 2**i

print(sum)

Buggy python submission (verdict: Time Limit Exceeded):
import copy
N,K=list(map(int,input().split()))
a=list(map(int,input().split()))

num=0
a_sum=[0]
for i in range(N):
  num+=a[i]
  a_sum.append(num)
  

#print(a_sum)

a_mat=[[0 for i in range(N)] for j in range(N)]
for i in range(N):
  for j in range(i,N):
    a_mat[i][j] = a_sum[j+1]-a_sum[i]
    

a_mat2=copy.deepcopy(a_mat)

maxbit=1
while True:
  if a_sum[N]<2**maxbit and a_sum[N]>=2**(maxbit-1): 
    break
  else:
    maxbit+=1
maxnum=0
num_rest=int(N*(N+1)/2)
num_rest_now=int(N*(N+1)/2)
for bit in range(maxbit):
  for i in range(N):
    for j in range (i,N):
      if a_mat[i][j]&(2**(maxbit-bit-1)) == 0 and a_mat[i][j]!=0:
        num_rest_now-=1
        a_mat2[i][j]=0
  #print(a_mat)
  #print(num_rest_now)
  if num_rest_now >= K:
    maxnum+=2**(maxbit-bit-1)
    a_mat=copy.deepcopy(a_mat2)
    num_rest=num_rest_now
  else:
    a_mat2=copy.deepcopy(a_mat)
    num_rest_now=num_rest
  
print(maxnum)
    

Fixed submission:
import sys
from collections import deque, defaultdict
import copy
input=sys.stdin.readline
sys.setrecursionlimit(10 ** 9)

N, K = list(map(int, input().split()))
a = list(map(int, input().split()))
sum_a = [0, a[0]]
for i in range(1, N):
    sum_a.append(sum_a[-1]+a[i])

bubunwa = []
for i in range(N):
    for j in range(i + 1, N + 1):
        bubunwa.append(sum_a[j] - sum_a[i])

max_bit = 2
while True:
    if sum_a[-1] < 2**max_bit:
        break
    max_bit += 1

sum = 0
for i in range(max_bit ,-1, -1):
    kouho = []
    for n in bubunwa:
        if n & 2**i == 2**i:
            kouho.append(n)
    if len(kouho) >= K:
        bubunwa = copy.deepcopy(kouho)
        sum += 2**i

print(sum)