<p>Given an integer array <code>nums</code> and an integer <code>k</code>, return <code>true</code> if it is possible to divide this array into <code>k</code> non-empty subsets whose sums are all equal.</p>

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

<pre>
<strong>Input:</strong> nums = [4,3,2,3,5,2,1], k = 4
<strong>Output:</strong> true
<strong>Explanation:</strong> It is possible to divide it into 4 subsets (5), (1, 4), (2,3), (2,3) with equal sums.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4], k = 3
<strong>Output:</strong> false
</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= nums.length &lt;= 16</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
	<li>The frequency of each element is in the range <code>[1, 4]</code>.</li>
</ul>

class Solution {
    unordered_map<int,bool> um;
    bool canSum(vector<int> &nums, int selected, int target, int cur_sum, int index, int k) {
        if (k == 1) {
            return true;
        }
        if (target == cur_sum) {
            return um[selected] = canSum (nums, selected, target, 0, 0, k-1);
        }
        if (um.count(selected)){
            return um[selected];
        }
        if (target < cur_sum) {
            return um[selected] = false;
        }
        for(int i = index; i < nums.size(); i++) {
            if (selected & (1<<i))
                continue;
            selected |= (1 << i);
            if (canSum (nums, selected, target, cur_sum + nums[i], i+1, k)) {
                return um[selected] = true;   
            }
            selected &= ~(1 << i);
        }      
        return um[selected] = false;
    }
public:
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        if (k == 1)
            return true;
        int sum = 0;
        for (int i = 0; i < nums.size(); i++) {
            sum += nums[i];
        }
        int target = sum / k;
        if (target * k != sum) {
            return false;
        }
        int selected = 0;
        std::sort(nums.begin(), nums.end(), std::greater<int>());
        return canSum(nums, selected, target, 0, 0, k);
    }
};
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