<p>You are given an integer array <code>prices</code> where <code>prices[i]</code> is the price of a given stock on the <code>i<sup>th</sup></code> day, and an integer <code>k</code>.</p>

<p>Find the maximum profit you can achieve. You may complete at most <code>k</code> transactions: i.e. you may buy at most <code>k</code> times and sell at most <code>k</code> times.</p>

<p><strong>Note:</strong> You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> k = 2, prices = [2,4,1]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Buy on day 1 (price = 2) and sell on day 2 (price = 4), profit = 4-2 = 2.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> k = 2, prices = [3,2,6,5,0,3]
<strong>Output:</strong> 7
<strong>Explanation:</strong> Buy on day 2 (price = 2) and sell on day 3 (price = 6), profit = 6-2 = 4. Then buy on day 5 (price = 0) and sell on day 6 (price = 3), profit = 3-0 = 3.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= 100</code></li>
	<li><code>1 &lt;= prices.length &lt;= 1000</code></li>
	<li><code>0 &lt;= prices[i] &lt;= 1000</code></li>
</ul>

class Trade:
    def __init__(self, buy, profit):
        self.buy = buy
        self.profit = profit
    def __str__(self):
        return f"T({self.buy},{self.profit})"
    def __repr__(self):
        return str(self)
class Minpx:
    def __init__(self, px, idx):
        self.px = px
        self.idx = idx
    def __repr__(self):
        return str(self)
    def __str__(self):
        return f"MP({self.px},{self.idx})"
class Solution:
    def maxProfit(self, k: int, prices: List[int]) -> int:
        mp = [Minpx(prices[0],0)]
        for i in range(1,len(prices)):
            if(mp[i-1].px > prices[i]):
                mp.append(Minpx(prices[i],i))
            else:
                mp.append(mp[-1])
        trds = [[] * len(prices)]
        for i in range(1, len(prices)):
            trds.append([])
            for j in range(0,i):
                profit = prices[i] - prices[j]
                if(profit > 0):
                    trds[i].append(Trade(j,profit))
                #j=mp[j].idx - 1

        #print(trds)
        dp = [[0] * (k+1) for _ in range(len(prices))]
        for pIdx in range(1,len(dp)):
            for trdNum in range(1,len(dp[0])):
                dp[pIdx][trdNum] = dp[pIdx-1][trdNum]
                for trd in trds[pIdx]:
                    dp[pIdx][trdNum] = max(dp[pIdx][trdNum], trd.profit + dp[trd.buy][trdNum-1])
        #print(dp)
        return dp[-1][-1]
45395