def solve():
N, K = map(int, input().split())
max_heap = OrderHeap([], lambda key: -key)
unique = set()
cnt = defaultdict(int)
max_heap.push(N)
cnt[N] = 1
while len(max_heap) > 0:
val = max_heap.pop()
nr = cnt[val]
if K <= nr:
return (val - 1 - (val-1)//2, (val - 1) // 2)
else:
K -= nr
unique.add(val)
l = [(val-1)//2, val - 1 - (val-1)//2]
for el in l:
if el:
if cnt[el] is 0:
max_heap.push(el)
cnt[el] += nr
def test_push(self):
heap = OrderHeap([], key=self.key)
wanted = set()
not_wanted = set(ascii_uppercase)
for c in reversed(ascii_uppercase):
heap.push(c)
wanted.add(c)
not_wanted.remove(c)
self.assertHeap(wanted, not_wanted, heap)
self.assertHeap(ascii_uppercase, [], heap)
def test_pushpop(self):
heap = OrderHeap(reversed(ascii_lowercase), key=self.key)
wanted = set(ascii_lowercase)
not_wanted = set()
for u, l in reversed(list(zip(ascii_uppercase, ascii_lowercase))):
self.assertEqual(l, heap.pushpop(u))
wanted.add(u)
wanted.remove(l)
not_wanted.add(l)
self.assertHeap(wanted, not_wanted, heap)
self.assertHeap(ascii_uppercase, ascii_lowercase, heap)
def test_pop(self):
heap = OrderHeap(reversed(ascii_uppercase), key=self.key)
wanted = set(ascii_uppercase)
not_wanted = set()
sorted_items = []
for c in reversed(ascii_uppercase):
self.assertEqual(c, heap.pop())
wanted.remove(c)
not_wanted.add(c)
self.assertHeap(wanted, not_wanted, heap)
sorted_items.append(c)
self.assertSequenceEqual(list(reversed(ascii_uppercase)), sorted_items)
self.assertHeap([], ascii_uppercase, heap)
def test_repr(self):
heap = OrderHeap(reversed(ascii_uppercase), key=self.key)
self.assertHeap(heap, [], eval(re.sub(r'key=<.*>', 'key=self.key', repr(heap))))
def test_remove_not_implemented(self):
heap = OrderHeap(reversed(ascii_uppercase), key=self.key)
self.assertRaises(NotImplementedError, heap.remove, 'A')
def test_pushpop_on_empty_heap(self):
self.assertEqual('A', OrderHeap(key=self.key).pushpop('A'))
def test_peek(self):
heap = OrderHeap(reversed(ascii_uppercase), key=self.key)
self.assertEqual('Z', heap.peek())
def test_check_variant_invalid(self):
heap = OrderHeap(ascii_uppercase, key=self.key)
heap[3] = (self.key('t'), 't')
self.assertRaises(InvalidHeapError, heap.check)
def test_check(self):
OrderHeap([], key=self.key).check()
OrderHeap(ascii_uppercase, key=self.key).check()
OrderHeap(reversed(ascii_uppercase), key=self.key).check()
def test_init(self):
self.assertHeap([], [], OrderHeap(key=self.key))
self.assertHeap([], [], OrderHeap([], key=self.key))
self.assertHeap(ascii_uppercase, [], OrderHeap(ascii_uppercase, key=self.key))