Buggy python submission (verdict: Time Limit Exceeded):
def main():
    from itertools import accumulate

    n, k = map(int, input().split())
    *a, = map(int, input().split())

    acc = (0,) + tuple(accumulate((a)))

    bits = [0] * 40

    seg_idx = 0
    for r in range(1, n + 1):
        for l in range(r):
            b = acc[r] - acc[l]
            for j in range(40):
                if (b >> j) & 1:
                    bits[j] |= (1 << seg_idx)
            seg_idx += 1

    ret = 0
    t = (1 << seg_idx) - 1
    for j in range(39, -1, -1):
        s = t & bits[j]
        if bin(s).count('1') >= k:
            ret |= (1 << j)
            t = s
    print(ret)


if __name__ == '__main__':
    main()


Fixed submission:
from math import log, ceil

n, k = map(int, input().split())
a = tuple(map(int, input().split()))

A_MAX = 10 ** 9
MAX_BIT_LENGTH = ceil(log(A_MAX * n, 2))

cs = [0]
t = 0
for aa in a:
    t += aa
    cs.append(t)

ps = []
for r in range(1, n + 1):
    for l in range(r):
        ps.append(cs[r] - cs[l])

ans = 0
for b in range(MAX_BIT_LENGTH)[::-1]:
    cnt = 0
    t = ans + (1 << b)
    for p in ps:
        if p & t == t:
            cnt += 1
            if cnt == k:
                ans = t
                break

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
def main():
    from itertools import accumulate

    n, k = map(int, input().split())
    *a, = map(int, input().split())

    acc = (0,) + tuple(accumulate(a))

    bs = tuple(set() for _ in range(40))

    pow2 = [1 << j for j in range(40)]

    m = 0
    for l in range(n):
        for r in range(l + 1, n + 1):
            beauty = acc[r] - acc[l]
            for j in range(40):
                if beauty & pow2[j] > 0:
                    bs[j].add(m)
            m += 1

    ret = 0
    t = set(range(m))
    for j in range(39, -1, -1):
        s = t & bs[j]
        if len(s) >= k:
            ret += pow2[j]
            t = s
    print(ret)


if __name__ == '__main__':
    main()


Fixed submission:
from math import log, ceil

n, k = map(int, input().split())
a = tuple(map(int, input().split()))

A_MAX = 10 ** 9
MAX_BIT_LENGTH = ceil(log(A_MAX * n, 2))

cs = [0]
t = 0
for aa in a:
    t += aa
    cs.append(t)

ps = []
for r in range(1, n + 1):
    for l in range(r):
        ps.append(cs[r] - cs[l])

ans = 0
for b in range(MAX_BIT_LENGTH)[::-1]:
    cnt = 0
    t = ans + (1 << b)
    for p in ps:
        if p & t == t:
            cnt += 1
            if cnt == k:
                ans = t
                break

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
from itertools import accumulate

n, k = map(int, input().split())
*a, = map(int, input().split())

acc = (0,) + tuple(accumulate(a))

bs = tuple(set() for _ in range(40))

m = 0
for l in range(n):
    for r in range(l + 1, n + 1):
        beauty = acc[r] - acc[l]
        for j in range(40):
            if beauty & (1 << j) > 0:
                bs[j].add(m)
        m += 1

ret = 0
t = set(range(m))
for j in range(39, -1, -1):
    s = t & bs[j]
    if len(s) >= k:
        ret += 1 << j
        t = s
print(ret)


Fixed submission:
from math import log, ceil

n, k = map(int, input().split())
a = tuple(map(int, input().split()))

A_MAX = 10 ** 9
MAX_BIT_LENGTH = ceil(log(A_MAX * n, 2))

cs = [0]
t = 0
for aa in a:
    t += aa
    cs.append(t)

ps = []
for r in range(1, n + 1):
    for l in range(r):
        ps.append(cs[r] - cs[l])

ans = 0
for b in range(MAX_BIT_LENGTH)[::-1]:
    cnt = 0
    t = ans + (1 << b)
    for p in ps:
        if p & t == t:
            cnt += 1
            if cnt == k:
                ans = t
                break

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
def b_len(v):
    return len(bin(v)[2:])


n, k = map(int, input().split())
a = list(map(int, input().split()))

cs = [0]
for aa in a:
    cs.append(cs[-1] + aa)

ps = []
for i in range(1, n + 1):
    for j in range(i):
        ps.append(cs[i] - cs[j])

ps = sorted(ps, reverse=True)

pw = b_len(ps[k - 1])
MOD = 2 ** pw

nps = {i:set() for i in range(pw)}
for i in range(len(ps)):
    t = ps[i] % MOD
    for j in range(pw):
        if 1 << j & t:
            nps[j].add(i)

ans = 0
buf = set(range(len(ps)))
for j in range(pw)[::-1]:
    if len(nps[j]) >= k:
        x = buf & nps[j]
        if len(x) >= k:
            buf = x
            ans += 2 ** j

print(ans)

Fixed submission:
from math import log, ceil

n, k = map(int, input().split())
a = tuple(map(int, input().split()))

A_MAX = 10 ** 9
MAX_BIT_LENGTH = ceil(log(A_MAX * n, 2))

cs = [0]
t = 0
for aa in a:
    t += aa
    cs.append(t)

ps = []
for r in range(1, n + 1):
    for l in range(r):
        ps.append(cs[r] - cs[l])

ans = 0
for b in range(MAX_BIT_LENGTH)[::-1]:
    cnt = 0
    t = ans + (1 << b)
    for p in ps:
        if p & t == t:
            cnt += 1
            if cnt == k:
                ans = t
                break

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
def b_len(v):
    return len(bin(v)[2:])


n, k = map(int, input().split())
a = list(map(int, input().split()))

cs = [0]
for aa in a:
    cs.append(cs[-1] + aa)

ps = []
for i in range(1, n + 1):
    for j in range(i):
        ps.append(cs[i] - cs[j])

ps = sorted(ps, reverse=True)

pw = b_len(ps[k - 1])
MOD = 2 ** pw

nps = [set() for _ in range(pw)]
len_nps = [0 for _ in range(len(nps))]
for i, p in enumerate(ps, 0):
    for j in range(pw):
        if 1 << j & p:
            nps[j].add(i)
            len_nps[j] += 1
ans = 0
buf = set(range(len(ps)))
for j in range(pw)[::-1]:
    if len_nps[j] >= k:
        x = buf & nps[j]
        if len(x) >= k:
            buf = x
            ans += 2 ** j

print(ans)

Fixed submission:
from math import log, ceil

n, k = map(int, input().split())
a = tuple(map(int, input().split()))

A_MAX = 10 ** 9
MAX_BIT_LENGTH = ceil(log(A_MAX * n, 2))

cs = [0]
t = 0
for aa in a:
    t += aa
    cs.append(t)

ps = []
for r in range(1, n + 1):
    for l in range(r):
        ps.append(cs[r] - cs[l])

ans = 0
for b in range(MAX_BIT_LENGTH)[::-1]:
    cnt = 0
    t = ans + (1 << b)
    for p in ps:
        if p & t == t:
            cnt += 1
            if cnt == k:
                ans = t
                break

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
def b_len(v):
    return len(bin(v)[2:])


n, k = map(int, input().split())
a = list(map(int, input().split()))

cs = [0]
for aa in a:
    cs.append(cs[-1] + aa)

ps = []
for i in range(1, n + 1):
    for j in range(i):
        ps.append(cs[i] - cs[j])

ps = sorted(ps, reverse=True)

pw = b_len(ps[k - 1])
MOD = 2 ** pw

nps = [set() for _ in range(pw)]
for i in range(len(ps)):
    t = ps[i] % MOD
    for j in range(pw):
        if 1 << j & t:
            nps[j].add(i)

ans = 0
buf = set(range(len(ps)))
for j in range(pw)[::-1]:
    if len(nps[j]) >= k:
        x = buf & nps[j]
        if len(x) >= k:
            buf = x
            ans += 2 ** j

print(ans)

Fixed submission:
from math import log, ceil

n, k = map(int, input().split())
a = tuple(map(int, input().split()))

A_MAX = 10 ** 9
MAX_BIT_LENGTH = ceil(log(A_MAX * n, 2))

cs = [0]
t = 0
for aa in a:
    t += aa
    cs.append(t)

ps = []
for r in range(1, n + 1):
    for l in range(r):
        ps.append(cs[r] - cs[l])

ans = 0
for b in range(MAX_BIT_LENGTH)[::-1]:
    cnt = 0
    t = ans + (1 << b)
    for p in ps:
        if p & t == t:
            cnt += 1
            if cnt == k:
                ans = t
                break

print(ans)