Subsequence of Size K With the Largest Even Sum
<p>You are given an integer array <code>nums</code> and an integer <code>k</code>. Find the <strong>largest even sum</strong> of any subsequence of <code>nums</code> that has a length of <code>k</code>.</p>

<p>Return <em>this sum, or </em><code>-1</code><em> if such a sum does not exist</em>.</p>

<p>A <strong>subsequence</strong> is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.</p>

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

<pre>
<strong>Input:</strong> nums = [4,1,5,3,1], k = 3
<strong>Output:</strong> 12
<strong>Explanation:</strong>
The subsequence with the largest possible even sum is [4,5,3]. It has a sum of 4 + 5 + 3 = 12.
</pre>

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

<pre>
<strong>Input:</strong> nums = [4,6,2], k = 3
<strong>Output:</strong> 12
<strong>Explanation:</strong>
The subsequence with the largest possible even sum is [4,6,2]. It has a sum of 4 + 6 + 2 = 12.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,3,5], k = 1
<strong>Output:</strong> -1
<strong>Explanation:</strong>
No subsequence of nums with length 1 has an even sum.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= k &lt;= nums.length</code></li>
</ul>
Greedy; Array; Sorting
function largestEvenSum(nums: number[], k: number): number {
    nums.sort((a, b) => a - b);
    let ans = 0;
    const n = nums.length;
    for (let i = 0; i < k; ++i) {
        ans += nums[n - i - 1];
    }
    if (ans % 2 === 0) {
        return ans;
    }
    const inf = 1 << 29;
    let mx1 = -inf,
        mx2 = -inf;
    for (let i = 0; i < n - k; ++i) {
        if (nums[i] % 2 === 1) {
            mx1 = nums[i];
        } else {
            mx2 = nums[i];
        }
    }
    let mi1 = inf,
        mi2 = inf;
    for (let i = n - 1; i >= n - k; --i) {
        if (nums[i] % 2 === 1) {
            mi2 = nums[i];
        } else {
            mi1 = nums[i];
        }
    }
    ans = Math.max(ans - mi1 + mx1, ans - mi2 + mx2);
    return ans < 0 ? -1 : ans;
}
