<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 {
public:
    int t = 0;
    unordered_set<int> c;
    bool dp(vector<int>& nums, int n, int x) {
        if(x == 0 && n == (1 << nums.size()) - 1) return true;
        if(c.count(n)) return false;
        if(!x) x = t;
        for(int i = 0; i < nums.size(); i++) {
            if(n & (1 << i)) continue;
            if(nums[i] > x) continue;
            if(dp(nums, n + (1 << i), x - nums[i])) return true;
        }
        c.insert(n);
        return false;
    }
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        if(nums.size() < k) return false;
        for(auto i : nums) t += i;
        if(t % k) return false;
        t /= k;
        for(auto i : nums) if(i > t) return false;
        return dp(nums, 0, t);
    }
};
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