The Ulam sequence `U` is defined by `u0 = u`, `u1 = v`, with the general term `uN` for `N > 2` given by the least integer expressible uniquely as the sum of two distinct earlier terms. In other words, the next number is always the smallest, unique sum of any two previous terms.

Complete the function that creates an Ulam Sequence starting with the given `u0` and `u1`, and contains `n` terms.

## Example

The first 10 terms of the sequence `U(u0=1, u1=2)` are: 1, 2, 3, 4, 6, 8, 11, 13, 16, 18.

Let's see it in details:
* The first term after the initial 1, 2 is obviously 3, because 1 + 2 = 3
* The next term is 1 + 3 = 4 (we don't have to worry about 4 = 2 + 2 since it is a sum of a *single term* instead of *distinct terms*)
* 5 is not a member of the sequence since it is representable in two ways: 1 + 4 and 2 + 3
* 6 is a memeber, as 2 + 4 = 6
* etc.


Description Reference: http://mathworld.wolfram.com/UlamSequence.html

---

Performance version: https://www.codewars.com/kata/ulam-sequences-performance-edition

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'def ulam_sequence(u0, u1, n):\n    """\n    Input\n    u0 = first number\n    u1 = second numberr\n    n  = number of elements in sequence\n    \n    Return\n    Ulam Sequence (u0, u1, u2...) with n-terms\n    """\n    U = [u0, u1]\n    next_num = u1 + 1\n    while len(U) < n:\n        count = 0\n        index = 0\n        for number in U:\n            if next_num - number in U and number != next_num/2:\n                count += 1\n            if count >= 3:\n                break\n        if count < 3 and count > 0:\n            U.append(next_num)\n        next_num += 1\n    return U'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'ulam_sequence'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 5720