<p>Given an integer array <code>arr</code> and an integer <code>k</code>, modify the array by repeating it <code>k</code> times.</p>

<p>For example, if <code>arr = [1, 2]</code> and <code>k = 3 </code>then the modified array will be <code>[1, 2, 1, 2, 1, 2]</code>.</p>

<p>Return the maximum sub-array sum in the modified array. Note that the length of the sub-array can be <code>0</code> and its sum in that case is <code>0</code>.</p>

<p>As the answer can be very large, return the answer <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> arr = [1,2], k = 3
<strong>Output:</strong> 9
</pre>

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

<pre>
<strong>Input:</strong> arr = [1,-2,1], k = 5
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr = [-1,-2], k = 7
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= k &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>4</sup> &lt;= arr[i] &lt;= 10<sup>4</sup></code></li>
</ul>

#if k==1 then kadanes algo

#now two cases :

'''
when sum<0:
then first two addition mein he hamara addition hoga

when sum>0:
then first and last addition and (k-2) * sum humara result hoga
'''
class Solution:
    def kConcatenationMaxSum(self, arr: List[int], k: int) -> int:
        sum_arr = sum(arr)
        def kadanes(arr):
            print(arr)
            max_sum=0
            sume=0
            for num in arr:
                sume+=num
                if sume<=0:
                    sume=max(num,0)
                max_sum = max(max_sum,sume)
            return max_sum%(10**9+7)
        
        if k==1:
            return kadanes(arr)
        arr1=arr+arr
        print(arr1)
        if sum_arr>=0:
            return kadanes(arr1)%(10**9+7)+ ((k-2)*sum_arr)%(10**9+7)
        return kadanes(arr1)%(10**9+7)
        
31600