Increasing COVID cases have created panic amongst the people of Chefland, so the government is starting to push for production of a vaccine. It has to report to the media about the exact date when vaccines will be available.
There are two companies which are producing vaccines for COVID. Company A starts producing vaccines on day $D_1$ and it can produce $V_1$ vaccines per day. Company B starts producing vaccines on day $D_2$ and it can produce $V_2$ vaccines per day. Currently, we are on day $1$.
We need a total of $P$ vaccines. How many days are required to produce enough vaccines? Formally, find the smallest integer $d$ such that we have enough vaccines at the end of the day $d$.

-----Input-----
- The first and only line of the input contains five space-separated integers $D_1$, $V_1$, $D_2$, $V_2$ and $P$.

-----Output-----
Print a single line containing one integer ― the smallest required number of days.

-----Constraints-----
- $1 \le D_1, V_1, D_2, V_2 \le 100$
- $1 \le P \le 1,000$

-----Subtasks-----
Subtask #1 (30 points): $D_1 = D_2$
Subtask #2 (70 points): original constraints

-----Example Input 1-----
1 2 1 3 14

-----Example Output 1-----
3

-----Explanation-----
Since $D_1 = D_2 = 1$, we can produce $V_1 + V_2 = 5$ vaccines per day. In $3$ days, we produce $15$ vaccines, which satisfies our requirement of $14$ vaccines.

-----Example Input 2-----
5 4 2 10 100

-----Example Output 2-----
9

-----Explanation-----
There are $0$ vaccines produced on the first day, $10$ vaccines produced on each of days $2$, $3$ and $4$, and $14$ vaccines produced on the fifth and each subsequent day. In $9$ days, it makes a total of $0 + 10 \cdot 3 + 14 \cdot 5 = 100$ vaccines.

```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

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = 'd1,v1,d2,v2,p=input().split()\nd1=int(d1)\nv1=int(v1)\nd2=int(d2)\nv2=int(v2)\np=int(p)\nif d1==d2:\n if p%(v1+v2)==0:\n  rd=int(p/(v1+v2))+d1-1\n else:\n  rd=int(p//(v1+v2))+d1\nelif d1<d2:\n dd=d2-d1\n vp=v1*dd\n if p<=dd:\n  if p%v1==0:\n   rd=int(p/v1)+d1-1\n  else:\n   rd=int(p//v1)+d1\n else:\n  vl=p-vp\n  if vl%(v1+v2)==0:\n   rd=int(vl/(v1+v2))+d2-1\n  else:\n   rd=int(vl//(v1+v2))+d2\nelse:\n dd=d1-d2\n vp=v2*dd\n if p<=vp:\n  if p%v2==0:\n   rd=int(p/v2)+d2-1\n  else:\n   rd=int(p//v2)+d2\n else:\n  vl=p-vp\n  if vl%(v1+v2)==0:\n   rd=int(vl/(v1+v2))+d1-1\n  else:\n   rd=int(vl//(v1+v2))+d1\nprint(rd)'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13559