<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>

class Solution {
public:
    int kConcatenationMaxSum(vector<int>& arr, int k) {
        long long answer = 0;
        long long sum = 0;
        for (const auto& x : arr) sum += x;
        answer = max(answer, 1ll * sum * k);
        long long mx = 0, pref = 0;
        for (const auto& x : arr) {
            pref += x;
            if (pref < 0) pref = 0;
            mx = max(mx, pref);
        }
        pref = 0;
        for (int i = arr.size() - 1; i >= 0; --i) {
            pref += arr[i];
            if (pref < 0) pref = 0;
            mx = max(mx, pref);
        }
        answer = max(answer, mx);
        if (sum >= 0) {
            answer = max(answer, 1ll * (k - 1) * sum + mx);
        }
        if (k >= 2) {
            vector<int> a;
            for (const auto& x : arr) a.push_back(x);
            for (const auto& x : arr) a.push_back(x);
            long long s = 0;
            for (const auto& x : a) {
                s += x;
                if (s < 0) s = 0;
                answer = max(answer, s);
            }
        }
        return answer % 1000000007;        
    }
};
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