You are a king and you are at war. If the enemy breaks through your frontline you lose.
Enemy can break the line only if the sum of morale of any $K$ continuous soldiers is strictly less than $M$. So, you being a motivational orator decides to boost their morale by giving a speech. On hearing it morale of a soldier multiplies by $X$ which depends on you and your speech (i.e. $X$ can be any positive value) but atmost only $K$ continuous speakers can hear your speech.
N soldiers are standing on the frontline with $A[i]$ morale. 
Determine the minimum number of speeches you need to give.

-----Input:-----
The first line contains three space seperated integers $N,K,M$.
The next line contains $N$ space integers, ith of which denotes the morale of $ith$ soldier.

-----Output:-----
Output the minimum number of speeches required. In case if it is impossible to achieve, print $-1$.

-----Constraints:-----
$1 \leq N,M \leq 10^5$
$1 \leq k \leq N$
$0 \leq Ai \leq 10^5$ 

-----Sample Input:-----
6 2 5
1 1 1 1 1 1

-----Sample Output:-----
2

-----Explanation:-----
We multiply 2nd ,3rd  and 5th,6th by 5. Resulting array will be 1 5 5 1 5 5.

```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 = "def main():\r\n    n,k,m = list(map(int,input().split()))\r\n    arr = list(map(int,input().split()))\r\n    dp = [-1]\r\n    for i in range(n):\r\n        if arr[i] > 0:\r\n            dp.append(i)\r\n        else:\r\n            dp.append(dp[-1])\r\n\r\n    dp.pop(0)\r\n    start = 0\r\n    count = 0\r\n    total = 0\r\n    ans = 0\r\n    index = -1\r\n    rem = k\r\n    #print(dp)\r\n    for i in range(n):\r\n        if index != -1:\r\n            if i-index <= rem:\r\n                #print('here',i,index)\r\n                arr[i] *= m\r\n            else:\r\n                index = -1\r\n                \r\n        total += arr[i]\r\n        count += 1\r\n        if count == k:\r\n            #print(total,start,i)\r\n            count -= 1\r\n            if total < m:\r\n                index = dp[i]\r\n                if index == -1 or i-index+1 > k:\r\n                    print(-1)\r\n                    return\r\n                \r\n                #print(index)\r\n                rem = k-(i-index+1)\r\n                #print('what',rem)\r\n                total -= arr[index]\r\n                arr[index] *= m\r\n                total += arr[index]\r\n                ans += 1\r\n                index = i\r\n\r\n            total -= arr[start]\r\n            start += 1\r\n\r\n    #print(arr)\r\n    print(ans)\r\n\r\nmain()\r\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14089