<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:
    unordered_map<int, int> dp;
    bool solve(int bitmask, int k, int sum, vector<int>& nums, int target, int index, int count) {
        if (count == k-1) return true;
        if (dp.find(bitmask) != dp.end()) return dp[bitmask];
        if (sum > target) return false;
        if (sum == target) {
            return dp[bitmask] = solve(bitmask, k, 0, nums, target, 0, count+1);
        }
        for (int j = index; j < nums.size(); j++) {
            if (!(bitmask & (1 << j))) {
                int newMask = bitmask | (1 << j);
                if (solve(newMask, k, sum+nums[j], nums, target, j+1, count)) {
                    return dp[bitmask] = true;
                }
            }
        }
        return dp[bitmask] = false;
    }
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        sort(nums.begin(), nums.end(), greater<int>());
        int sum = 0;
        for (int i = 0; i < nums.size(); i++) {
            sum += nums[i];
        }
        if (sum % k) return false;
        int target = sum / k;
        return solve(0, k, 0, nums, target, 0, 0);
    }
};
32641