You are given an integer array prices where prices[i] is the price of a given stock on the ith day, and an integer k.

Find the maximum profit you can achieve. You may complete at most k transactions.

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

**Example 1:**

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

**Example 2:**

**Input:** k = 2, prices = [3,2,6,5,0,3]
**Output:** 7
**Explanation:** 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.

**Constraints:**

0 <= k <= 100

0 <= prices.length <= 1000

0 <= prices[i] <= 1000

**Solution**:

```
class Solution
{
public int maxProfit(int k, int[] prices)
{
if(prices.length<2) return 0;
int havingstock;
int[][] nothavingstock = new int[k+1][prices.length+1];
for(int t=1;t<=k;t++)
{
havingstock = -prices[0];
for(int i=1;i<prices.length;i++)
{
havingstock = Math.max(havingstock,nothavingstock[t-1][i-1]-prices[i]);
nothavingstock[t][i] = Math.max(nothavingstock[t][i-1],havingstock+prices[i]);
}
}
return nothavingstock[k][prices.length-1];
}
}
```

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