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 NOD(self, a, b):\n        if a == b:\n            return a\n        c = max(a,b)\n        d = a + b - c\n        c = c%d\n        c = c if c>0 else d\n        return self.NOD(c,d)\n    def nthMagicalNumber(self, N: int, A: int, B: int) -> int:\n        const = 10**9 + 7\n        nod = self.NOD(A, B)\n        nok = int(A*B/nod)\n        C, D = min(A, B), max(A, B)\n        k_C = nok//C\n        k_D = nok//D\n        k = k_C + k_D - 1\n        div = N//k\n        mod = N - div*k\n        k_C_cur = (mod*k_C)//k\n        k_D_cur = mod - k_C_cur\n        #print(k_C, k_D, k, div, mod, k_C_cur, k_D_cur)\n        while True:\n            C_num = k_C_cur*C\n            D_num = k_D_cur*D\n            if -C < C_num - D_num < D:\n                return (div*nok + max(C_num, D_num))%const\n            elif C_num - D_num <= -C:\n                k_D_cur -= 1\n                k_C_cur += 1\n            else:\n                k_D_cur += 1\n                k_C_cur -= 1'
_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: 5996