def test_dup_integrate():
assert dup_integrate([], 1, QQ) == []
assert dup_integrate([], 2, QQ) == []
assert dup_integrate([QQ(1)], 1, QQ) == [QQ(1), QQ(0)]
assert dup_integrate([QQ(1)], 2, QQ) == [QQ(1, 2), QQ(0), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 0, QQ) == [QQ(1), QQ(2), QQ(3)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 1, QQ) == [QQ(1, 3), QQ(1), QQ(3), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 2, QQ) == [QQ(1, 12), QQ(1, 3), QQ(3, 2), QQ(0), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 3, QQ) == [QQ(1, 60), QQ(1, 12), QQ(1, 2), QQ(0), QQ(0), QQ(0)]
assert dup_integrate(dup_from_raw_dict({29: QQ(17)}, QQ), 3, QQ) == dup_from_raw_dict({32: QQ(17, 29760)}, QQ)
assert dup_integrate(dup_from_raw_dict({29: QQ(17), 5: QQ(1, 2)}, QQ), 3, QQ) == dup_from_raw_dict(
{32: QQ(17, 29760), 8: QQ(1, 672)}, QQ
)
def test_dup_integrate():
assert dup_integrate([], 1, QQ) == []
assert dup_integrate([], 2, QQ) == []
assert dup_integrate([QQ(1)], 1, QQ) == [QQ(1), QQ(0)]
assert dup_integrate([QQ(1)], 2, QQ) == [QQ(1, 2), QQ(0), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 0, QQ) == \
[QQ(1), QQ(2), QQ(3)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 1, QQ) == \
[QQ(1, 3), QQ(1), QQ(3), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 2, QQ) == \
[QQ(1, 12), QQ(1, 3), QQ(3, 2), QQ(0), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 3, QQ) == \
[QQ(1, 60), QQ(1, 12), QQ(1, 2), QQ(0), QQ(0), QQ(0)]
assert dup_integrate(dup_from_raw_dict({29: QQ(17)}, QQ), 3, QQ) == \
dup_from_raw_dict({32: QQ(17, 29760)}, QQ)
assert dup_integrate(dup_from_raw_dict({29: QQ(17), 5: QQ(1, 2)}, QQ), 3, QQ) == \
dup_from_raw_dict({32: QQ(17, 29760), 8: QQ(1, 672)}, QQ)