Buggy python submission (verdict: Time Limit Exceeded):
from collections import Counter


def check(ans, s):
    ret = 0
    for k, v in Sumdic.items():
        if ans & k != ans:
            continue
        ret += v
        if ret >= s:
            return True
    return False


n, k = map(int, input().split())
A = list(map(int, input().split()))
sumA = [0]
for i in range(len(A)):
    sumA.append(sumA[i] + A[i])

sumdic = [0] * (n * (n + 1) // 2)
kk = 0
for i in range(len(A)):
    # print(kk, sumdic)
    for j in range(i + 1, len(A) + 1):
        tmp = sumA[j] - sumA[i]
        sumdic[kk + j - 1 - i] = tmp
        # print(i, j)
    kk += n - i

# print(A)
# print(Counter(sumdic))
Sumdic = Counter(sumdic)

for i in reversed(range(len(format(sumA[-1], "b")))):
    # print(i)
    if check(2 ** i, k) is True:
        ans = 2 ** i
        tmp = i
        break
else:
    print(0)
    exit()

tmp -= 1
while(tmp != -1):
    if check(ans + 2 ** tmp, k) is True:
        ans += 2 ** tmp
    tmp -= 1
print(ans)

Fixed submission:
def check(ans, s):
    ret = 0
    for k in sumdic:
        if ans & k != ans:
            continue
        ret += 1
        if ret >= s:
            return True
    return False


n, k = map(int, input().split())
A = list(map(int, input().split()))
sumA = [0]
for i in range(len(A)):
    sumA.append(sumA[i] + A[i])

sumdic = [0] * (n * (n + 1) // 2)
kk = 0
for i in range(len(A)):
    # print(kk, sumdic)
    for j in range(i + 1, len(A) + 1):
        tmp = sumA[j] - sumA[i]
        sumdic[kk + j - 1 - i] = tmp
        # print(i, j)
    kk += n - i

# print(A)
# print(Counter(sumdic))
# Sumdic = Counter(sumdic)

for i in reversed(range(len(format(sumA[-1], "b")))):
    # print(i)
    if check(2 ** i, k) is True:
        ans = 2 ** i
        tmp = i
        break
else:
    print(0)
    exit()

tmp -= 1
while(tmp != -1):
    if check(ans + 2 ** tmp, k) is True:
        ans += 2 ** tmp
    tmp -= 1
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
def check(ans, s):
    ret = 0
    for k, v in sumdic.items():
        if ans & k != ans:
            continue
        ret += v
        if ret >= s:
            return True
    return False


n, k = map(int, input().split())
A = list(map(int, input().split()))
sumA = [0]
for i in range(len(A)):
    sumA.append(sumA[i] + A[i])

sumdic = {}
for i in range(len(A)):
    for j in range(i + 1, len(A) + 1):
        tmp = sumA[j] - sumA[i]
        sumdic[tmp] = sumdic.get(tmp, 0) + 1
        # print(i, j)

# print(A)
# print(sumdic)

for i in reversed(range(len(format(sumA[-1], "b")))):
    # print(i)
    if check(2 ** i, k) is True:
        ans = 2 ** i
        tmp = i
        break
else:
    print(0)
    exit()

tmp -= 1
while(tmp != 0):
    if check(ans + 2 ** tmp, k) is True:
        ans += 2 ** tmp
    tmp -= 1
print(ans)

Fixed submission:
def check(ans, s):
    ret = 0
    for k in sumdic:
        if ans & k != ans:
            continue
        ret += 1
        if ret >= s:
            return True
    return False


n, k = map(int, input().split())
A = list(map(int, input().split()))
sumA = [0]
for i in range(len(A)):
    sumA.append(sumA[i] + A[i])

sumdic = [0] * (n * (n + 1) // 2)
kk = 0
for i in range(len(A)):
    # print(kk, sumdic)
    for j in range(i + 1, len(A) + 1):
        tmp = sumA[j] - sumA[i]
        sumdic[kk + j - 1 - i] = tmp
        # print(i, j)
    kk += n - i

# print(A)
# print(Counter(sumdic))
# Sumdic = Counter(sumdic)

for i in reversed(range(len(format(sumA[-1], "b")))):
    # print(i)
    if check(2 ** i, k) is True:
        ans = 2 ** i
        tmp = i
        break
else:
    print(0)
    exit()

tmp -= 1
while(tmp != -1):
    if check(ans + 2 ** tmp, k) is True:
        ans += 2 ** tmp
    tmp -= 1
print(ans)