<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 {
    bool solve(vector<int>&nums, int target, int sum, int k, bitset<16>&mask, vector<int>&dp){
        if(k == 1)return true;
        long long maskval = mask.to_ulong();
        if(dp[maskval] != -1)return dp[maskval] == 1;
        if(sum == target){
            return dp[maskval] = solve(nums, target, 0, k-1, mask, dp);
        }
        for(int i = 0; i<nums.size(); i++){
            if(sum+nums[i]<=target && mask[i] == 0){
                mask[i] = 1;
                if(solve(nums, target, sum+nums[i], k, mask, dp)){dp[maskval] = 1; return true;}
                mask[i] = 0;
            }
        }
        dp[maskval] = 0;
        return false;
    }
    
public:
    bool canPartitionKSubsets(vector<int>& nums, int k) {
        int n = nums.size();
        int sum = 0;
        for(int i = 0 ;i<n; i++){
            sum += nums[i];
        }
        if(sum%k)return false;
        int target = sum/k;
        bitset<16>mask;
        // cout<<mask<<endl;
        // mask[3] = 1;
        // cout<<mask.to_ulong()<<endl;
        vector<int>dp((1<<(n+1)), -1);
        // return false;
        return solve(nums, target, 0, k, mask, dp);
    }
};
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