There are N piles of stones arranged in a row.  The i-th pile has stones[i] stones.
A move consists of merging exactly K consecutive piles into one pile, and the cost of this move is equal to the total number of stones in these K piles.
Find the minimum cost to merge all piles of stones into one pile.  If it is impossible, return -1.
 

Example 1:
Input: stones = [3,2,4,1], K = 2
Output: 20
Explanation: 
We start with [3, 2, 4, 1].
We merge [3, 2] for a cost of 5, and we are left with [5, 4, 1].
We merge [4, 1] for a cost of 5, and we are left with [5, 5].
We merge [5, 5] for a cost of 10, and we are left with [10].
The total cost was 20, and this is the minimum possible.


Example 2:
Input: stones = [3,2,4,1], K = 3
Output: -1
Explanation: After any merge operation, there are 2 piles left, and we can't merge anymore.  So the task is impossible.


Example 3:
Input: stones = [3,5,1,2,6], K = 3
Output: 25
Explanation: 
We start with [3, 5, 1, 2, 6].
We merge [5, 1, 2] for a cost of 8, and we are left with [3, 8, 6].
We merge [3, 8, 6] for a cost of 17, and we are left with [17].
The total cost was 25, and this is the minimum possible.

 
Note:

1 <= stones.length <= 30
2 <= K <= 30
1 <= stones[i] <= 100

```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 mergeStones(self, stones: List[int], K: int) -> int:\n        # Time Complexity: O(N^3 K)\n        # Space Complexity: O(N^2 K)\n        \n        self.dp = {}\n        self.prefix = [0] + list(itertools.accumulate(stones))\n        \n        ret = self.merge(stones, 0, len(stones) - 1, 1, K)\n        \n        return ret\n        \n    def merge(self, stones, start: int, end: int, num_parts: int, K: int):\n        if (start, end, num_parts) in self.dp:\n            return self.dp[(start, end, num_parts)]\n        \n        if end - start + 1 < num_parts:\n            return -1\n        \n        if end - start + 1 == num_parts:\n            return 0\n        \n        window_sum = self.prefix[end + 1] - self.prefix[start] \n        \n        if num_parts == 1:\n            split = self.merge(stones, start, end, K, K)\n            \n            if split == -1:\n                ret = -1\n            else:\n                ret = window_sum + split\n        else:\n            candidates = []\n            \n            for i in range(start, end):\n                left = self.merge(stones, start, i, 1, K)\n                right = self.merge(stones, i + 1, end, num_parts - 1, K)\n                \n                \n                if left >= 0 and right >= 0:\n                    candidates.append(left + right)\n            \n            if candidates:\n                ret = min(candidates)\n            else:\n                ret = -1\n                \n        self.dp[(start, end, num_parts)] = ret\n        return ret\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'mergeStones'
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: 7924