A positive integer is magical if it is divisible by either A or B.
Return the N-th magical number.  Since the answer may be very large, return it modulo 10^9 + 7.
 



Example 1:
Input: N = 1, A = 2, B = 3
Output: 2


Example 2:
Input: N = 4, A = 2, B = 3
Output: 6


Example 3:
Input: N = 5, A = 2, B = 4
Output: 10


Example 4:
Input: N = 3, A = 6, B = 4
Output: 8

 
Note:

1 <= N <= 10^9
2 <= A <= 40000
2 <= B <= 40000

```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 = 'class Solution:\n    def nthMagicalNumber(self, N: int, A: int, B: int) -> int:\n        \n#         # O(N) solution -- TLE\n#         i = 1 # multiplier of A\n#         j = 1 # multiplier of B\n        \n#         res = 0\n        \n#         while N>0:\n#             if A*i < B*j:\n#                 res = A*i\n#                 i += 1\n#             elif A*i > B*j:\n#                 res = B*j\n#                 j += 1\n#             else:\n#                 res = A*i\n#                 i += 1\n#                 j += 1\n#             N-=1\n        \n#         return res%(10**9+7)\n    \n        # O(logN) solution -- binary search\n        def min_common_divisor(a, b):\n            less = min(a, b)\n            more = max(a, b)\n            for i in range(1, less+1):\n                if more*i % less == 0:\n                    return more*i\n            return a*b\n        \n        _cd = min_common_divisor(A, B)\n\n        min_ = min(A, B)\n        l, r = min_, min_*N+1\n        while l<r:\n            m = (l+r)>>1\n\n            if m//A+m//B-m//_cd < N:\n                l = m + 1\n            elif m//A+m//B-m//_cd > N:\n                r = m\n            else:\n                if m%A==0 and m%B==0:\n                    return m % (10**9+7)\n                else:\n                    r = m\n\n        return l % (10**9+7)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'nthMagicalNumber'
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: 5768